Algebra 1 Common Core

Problem 1

Simplify each expression.
$$
2^{-5}
$$

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00:23

Problem 2

Simplify each expression.
$$
m^{0}
$$

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00:55

Problem 3

Simplify each expression.
$$
5 s^{2} t^{-1}
$$

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00:38

Problem 4

Simplify each expression.
$$
\frac{4}{x^{-3}}
$$

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01:12

Problem 5

Evaluate each expression for $a=2$ and $b=-4$
$$
\text { Evaluate each expression for } a=2 \text { and } b=-4
$$

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01:25

Problem 6

Evaluate each expression for $a=2$ and $b=-4$
$$
2 a^{-4} b^{0}
$$

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00:51

Problem 7

Vocabulary A positive exponent shows repeated multiplication. What repeated operation does a negative exponent show?

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00:51

Problem 8

Error Analysis A student incorrectly simplified $\frac{x^{n}}{a-n n^{0} r}$ as shown below. Find and correct the student's error.

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Problem 9

Simplify each expression.
$$
3^{-2}
$$

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00:34

Problem 10

Simplify each expression.
$$
(-4.25)^{0}
$$

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00:40

Problem 11

Simplify each expression.
$$
(-5)^{-2}
$$

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Problem 12

Simplify each expression.
$$
-5^{-2}
$$

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00:38

Problem 13

Simplify each expression.
$$
(-4)^{-2}
$$

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00:29

Problem 14

Simplify each expression.
$$
2^{-6}
$$

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00:36

Problem 15

Simplify each expression.
$$
-3^{0}
$$

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00:46

Problem 16

Simplify each expression.
$$
-12^{-1}
$$

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00:20

Problem 17

Simplify each expression.
$$
\frac{1}{2^{0}}
$$

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00:24

Problem 18

Simplify each expression.
$$
58^{-1}
$$

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00:53

Problem 19

Simplify each expression.
$$
1.5^{-2}
$$

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00:45

Problem 20

Simplify each expression.
$$
(-5)^{-3}
$$

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00:33

Problem 21

Simplify each expression.
$$
4 a b^{0}
$$

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00:22

Problem 22

Simplify each expression.
$$
\frac{1}{x^{-7}}
$$

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00:25

Problem 23

Simplify each expression.
$$
5 x^{-4}
$$

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00:28

Problem 24

Simplify each expression.
$$
\frac{1}{c^{-1}}
$$

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Problem 25

Simplify each expression.
$$
\frac{3^{-2}}{n}
$$

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00:44

Problem 26

Simplify each expression.
$$
k^{-4} j^{0}
$$

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00:30

Problem 27

Simplify each expression.
$$
\frac{3 x^{-2}}{y}
$$

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Problem 28

Simplify each expression.
$$
\frac{7 a b^{-2}}{3 w}
$$

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00:32

Problem 29

Simplify each expression.
$$
c^{-5} d^{-7}
$$

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00:33

Problem 30

Simplify each expression.
$$
c^{-5} d^{7}
$$

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00:43

Problem 31

Simplify each expression.
$$
\frac{8}{2 s^{-3}}
$$

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00:49

Problem 32

Simplify each expression.
$$
\frac{7 s}{5 t^{-3}}
$$

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01:06

Problem 33

Simplify each expression.
$$
\frac{6 a^{-1} c^{-3}}{d^{0}}
$$

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01:11

Problem 34

Simplify each expression.
$$
2^{-3} x^{2} z^{-7}
$$

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01:07

Problem 35

Simplify each expression.
$$
12^{0} t^{7} u^{-11}
$$

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01:27

Problem 36

Simplify each expression.
$$
\frac{7 s^{0} t^{-5}}{2^{-1} m^{2}}
$$

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Problem 37

Evaluate each expression for $r=-3$ and $s=5$
$$
r^{-3}
$$

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00:43

Problem 38

Evaluate each expression for $r=-3$ and $s=5$
$$
s^{-3}
$$

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01:52

Problem 39

Evaluate each expression for $r=-3$ and $s=5$
$$
\frac{3 r}{s^{-2}}
$$

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01:02

Problem 40

Evaluate each expression for $r=-3$ and $s=5$
$$
\frac{s^{0}}{r^{-2}}
$$

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00:44

Problem 41

Evaluate each expression for $r=-3$ and $s=5$
$$
4 s^{-1}
$$

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01:15

Problem 42

Evaluate each expression for $r=-3$ and $s=5$
$$
r^{0} s^{-2}
$$

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01:23

Problem 43

Evaluate each expression for $r=-3$ and $s=5$
$$
r^{-4} s^{2}
$$

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01:50

Problem 44

Evaluate each expression for $r=-3$ and $s=5$
$$
2^{-4} r^{3} s^{-2}
$$

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01:41

Internet Traffic The number of visitors to a certain web site triples every month. The number of visitors is modeled by the expression $8100 \cdot 3^{m}$, where $m$ is the number of months after the number of visitors was measured. Evaluate the expression $m=-4 .$ What does the value of the expression represent in the situation?

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02:28

Problem 46

Population Growth A Galápagos cactus finch population increases by half every decade. The number of finches is modeled by the expression $45 \cdot 1.5^{d},$ where $d$ is the number of decades after the population was measured. Evaluate the expression for $d=-2, d=0$, and $d=1 .$ What does each value of the expression represent in the situation?

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Problem 47

Mental Math Is the value of each expression positive or negative?
$$
-2^{2}
$$

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00:33

Problem 48

Mental Math Is the value of each expression positive or negative?
$$
(-2)^{2}
$$

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00:47

Problem 49

Mental Math Is the value of each expression positive or negative?
$$
(-2)^{3}
$$

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01:14

Problem 50

Mental Math Is the value of each expression positive or negative?
$$
(-2)^{-3}
$$

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Problem 51

Write each number as a power of 10 using negative exponents.
$$
\frac{1}{10}
$$

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00:37

Problem 52

Write each number as a power of 10 using negative exponents.
$$
\frac{1}{100}
$$

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00:49

Problem 53

Write each number as a power of 10 using negative exponents.
$$
\frac{1}{1000}
$$

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00:51

Problem 54

Write each number as a power of 10 using negative exponents.
$$
\frac{1}{10,000}
$$

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02:00

Problem 55

a. Patterns Complete the pattern using powers of 5.
$$
\frac{1}{5^{2}}=\mathbb{} \quad \frac{1}{5^{1}}=\mathbb{} \quad \frac{1}{5^{0}}=\mathbb{} \quad \frac{1}{5^{-1}}=\mathbb{} \quad \frac{1}{5^{2}}=\mathbb{}
$$
b. Write $\frac{1}{5^{4}}$ using a positive exponent.
c. Rewrite $\frac{1}{a^{-n}}$ as a power of $a$.

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00:23

Problem 56

Rewrite each fraction with all the variables in the numerator.
$$
\frac{a}{b^{-2}}
$$

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Problem 57

Rewrite each fraction with all the variables in the numerator.
$$
\frac{4 g}{h^{3}}
$$

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00:49

Problem 58

Rewrite each fraction with all the variables in the numerator.
$$
\frac{5 m^{6}}{3 n}
$$

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00:57

Problem 59

Rewrite each fraction with all the variables in the numerator.
$$
\frac{8 c^{5}}{11 d^{4} e^{-2}}
$$

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04:01

Problem 60

Think About a Plan Suppose your drama club's budget doubles every year. This year the budget is 500 .dollar How much was the club's budget 2 yr ago? $\cdot$ What epression models what the budget of the club will be in $1 \mathrm{yr} ?$
In $2 \mathrm{yr}$ ? In years? $\cdot$ What value fy can you substitute into your expression to find the budget of the club $2 \mathrm{yr}$ ago?

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01:43

Problem 61

Copy and complete the table at the right.
(Table cannot copy)

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01:32

Problem 62

a. Simplify $a^{n} \cdot a^{-n}$. b. Reasoning what is the mathematical relationship between $a^{n}$ and $a^{-n}$ ? Explain.

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01:41

Problem 63

Open-Ended Choose a fraction to use as a value for the variable $a$. Find the values of $a^{-1}, a^{2},$ and $a^{-2}$.

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01:56

Problem 64

Manufacturing A company is making metal rods with a target diameter of 1.5 $\mathrm{mm}$. A rod is acceptable when its diameter is within $10^{-3} \mathrm{mm}$ of the target diameter. Write an inequality for the acceptable range of diameters.

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Problem 65

Reasoning Are $3 x^{-2}$ and $3 x^{2}$ reciprocals? Explain.

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00:31

Problem 66

Simplify each expression.
$$
\left(\frac{r^{-7} b^{-8}}{t^{-4} u^{1}}\right)^{0}
$$

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01:10

Problem 67

Simplify each expression.
$$
(-5)^{2}-(0.5)^{-2}
$$

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01:20

Problem 68

Simplify each expression.
$$
\frac{6}{m^{2}}+\frac{5 m^{-2}}{3^{-3}}
$$

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00:45

Problem 69

Simplify each expression.
$$
2^{3}\left(5^{0}-6 m^{2}\right)
$$

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01:43

Problem 70

Simplify each expression.
$$
\frac{2 x^{-5} y^{3}}{n^{2}} \div \frac{r^{2} y^{5}}{2 n}
$$

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01:31

Problem 71

Simplify each expression.
$$
2^{-1}-\frac{1}{3^{-2}}+5\left(\frac{1}{2^{2}}\right)
$$

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01:18

Problem 72

For what value or values of $n$ is $n^{-3}=\left(\frac{1}{n}\right)^{5} ?$

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Problem 73

What is the simplified form of $-6(-6)^{-1} ?$

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01:13

Problem 74

Segment CD represents the flight of a bird that passes through the points $(1,2)$ and $(5,4)$. What is the slope of a line that represents the flight of a second bird that flew perpendicular to the first bird?

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01:19

Problem 75

What is the solution of the equation $1.5(x-2.5)=3 ?$

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Problem 76

What is the simplified form of $|3.5-4.7|+5.6 ?$

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01:10

Problem 77

What is the $y$ -intercept of the graph of $3 x-2 y=-8 ?$

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03:06

Problem 78

Solve each system by graphing.
$$
\begin{array}{l}{y>3 x+4} \\ {y \leq-3 x+1}\end{array}
$$

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02:56

Problem 79

Solve each system by graphing.
$$
\begin{array}{l}{y \leq-2 x+1} \\ {y<2 x-1}\end{array}
$$

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03:10

Problem 80

Solve each system by graphing.
$$
\begin{array}{l}{y \geq 0.5 x} \\ {y \leq x+2}\end{array}
$$

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Numerade Educator

00:29

Problem 81

Write an equation in slope-intercept form for the line with the given slope $m$ and $y$ -intercept $b$.
$$
m=-1, b=4
$$

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00:38

Problem 82

Write an equation in slope-intercept form for the line with the given slope $m$ and $y$ -intercept $b$.
$$
m=5, b=-2
$$

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00:50

Problem 82

Write an equation in slope-intercept form for the line with the given slope $m$ and $y$ -intercept $b$.
$$
m=5, b=-2
$$

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