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Section 1
Multiplication Rules for Exponents
Fill in the blank.Expressions such as $x^{4}, 10^{3},$ and $(5 t)^{2}$ are called _____ expressions.
Fill in the blank.Match each expression with the proper description.$$\left(a^{4} b^{2}\right)^{5} \quad\left(a^{8}\right)^{4} \quad a^{5} \cdot a^{3}$$a. Product of exponential expressions with the same baseb. Power of an exponential expressionc. Power of a product
Fill in the blanks.a. $(3 x)^{4}=$$\text{__}\cdot\text{__}\cdot\text{__}\cdot\text{__}$b. $(-5 y)(-5 y)(-5 y)=$_____
Fill in the blanks.a. $x=x^{\square{}}$b. $x^{m} x^{n}=\square$c. $(x y)^{n}=\square$d. $\left(a^{b}\right)^{c}=\square$
To simplify each expression, determine whether you add, subtract, multiply, or divide the exponents.a. $b^{6} \cdot b^{9}$b. $\left(n^{8}\right)^{4}$c. $\left(a^{4} b^{2}\right)^{5}$
To simplify $\left(2 y^{3} z^{2}\right)^{4},$ what factors within the parentheses must be raised to the fourth power?
Simplify each expression, if possible.$$\text { a. } x^{2}+x^{2}$$$$\text { b. } x^{2} \cdot x^{2}$$
Simplify each expression, if possible.$$\text { a. } x^{2}+x$$$$\text { b. } x^{2} \cdot x$$
Simplify each expression, if possible.$$\text { a. } x^{3}-x^{2}$$$$\text { b. } x^{3} \cdot x^{2}$$
Simplify each expression, if possible.$$\text { a. } 4^{2} \cdot 2^{4}$$$$\text { b. } x^{3} \cdot y^{2}$$
Complete each solution to simplify each expression.$$\begin{aligned}\left(x^{4} x^{2}\right)^{3} &=(\square)^{3} \\&=x^{\square}\end{aligned}$$
Complete each solution to simplify each expression.$$\begin{array}{l}\left(x^{4}\right)^{3}\left(x^{2}\right)^{3} \\\quad=x^{\square} \\\quad=x^{\square}\end{array} \cdot x^{6}$$
Identify the base and the exponent in each expression.$$4^{3}$$
Identify the base and the exponent in each expression.$$(-8)^{2}$$
Identify the base and the exponent in each expression.$$x^{5}$$
$$\left(\frac{5}{x}\right)^{3}$$
Identify the base and the exponent in each expression.$$(-3 x)^{2}$$
Identify the base and the exponent in each expression.$$(2 x y)^{10}$$
Identify the base and the exponent in each expression.$$-\frac{1}{3} y^{6}$$
Identify the base and the exponent in each expression.$$-x^{4}$$
Identify the base and the exponent in each expression.$$9 m^{12}$$
Identify the base and the exponent in each expression.$$3.14 r^{4}$$
Identify the base and the exponent in each expression.$$(y+9)^{4}$$
Identify the base and the exponent in each expression.$$(z-2)^{3}$$
Write each expression in an equivalent form using an exponent.$$m \cdot m \cdot m \cdot m \cdot m$$
Write each expression in an equivalent form using an exponent.$$r \cdot r \cdot r \cdot r \cdot r \cdot r$$
Write each expression in an equivalent form using an exponent.$$4 t \cdot 4 t \cdot 4 t \cdot 4 t$$
Write each expression in an equivalent form using an exponent.$$-5 u(-5 u)(-5 u)(-5 u)(-5 u)$$
Write each expression in an equivalent form using an exponent.$$4 \cdot t \cdot t \cdot t \cdot t \cdot t$$
Write each expression in an equivalent form using an exponent.$$5 \cdot u \cdot u \cdot u$$
Write each expression in an equivalent form using an exponent. $$a \cdot a \cdot b \cdot b \cdot b$$
Write each expression in an equivalent form using an exponent.$$m \cdot m \cdot m \cdot n \cdot n$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$5^{3} \cdot 5^{4}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$3^{4} \cdot 3^{6}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$a^{3} \cdot a^{3}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$m^{7} \cdot m^{7}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$b b^{2} b^{3}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$a a^{3} a^{5}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$\left(c^{5}\right)\left(c^{8}\right)$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$\left(d^{4}\right)\left(d^{20}\right)$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$\left(a^{2} b^{3}\right)\left(a^{3} b^{3}\right)$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$\left(u^{3} v^{5}\right)\left(u^{4} v^{5}\right)$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$c d^{4} \cdot c d$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$a b^{3} \cdot a b^{4}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$x^{2} \cdot y \cdot x \cdot y^{10}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$x^{3} \cdot y \cdot x \cdot y^{12}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$m^{100} \cdot m^{100}$$
Use the product rule for exponents to simplify each expression. Write the results using exponents.$$n^{600} \cdot n^{600}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left(3^{2}\right)^{4}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left(4^{3}\right)^{3}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left[(-4.3)^{3}\right]^{8}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left[(-1.7)^{9}\right]^{8}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left(m^{50}\right)^{10}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left(n^{25}\right)^{4}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left(y^{5}\right)^{3}$$
Use the power rule for exponents to simplify each expression. Write the results using exponents.$$\left(b^{3}\right)^{6}$$
Use the product and power rules for exponents to simplify each expression.$$\left(x^{2} x^{3}\right)^{5}$$
Use the product and power rules for exponents to simplify each expression.$$\left(y^{3} y^{4}\right)^{4}$$
$$\left(p^{2} p^{3}\right)^{5}$$
Use the product and power rules for exponents to simplify each expression.$$\left(r^{3} r^{4}\right)^{2}$$
Use the product and power rules for exponents to simplify each expression.$$\left(r^{3}\right)^{4}\left(t^{2}\right)^{3}$$
Use the product and power rules for exponents to simplify each expression.$$\left(b^{2}\right)^{5}\left(b^{3}\right)^{2}$$
Use the product and power rules for exponents to simplify each expression.$$\left(u^{4}\right)^{2}\left(u^{3}\right)^{2}$$
Use the product and power rules for exponents to simplify each expression.$$\left(v^{5}\right)^{2}\left(v^{3}\right)^{4}$$
Use the power of a product rule for exponents to simplify each expression.$$(6 a)^{2}$$
Use the power of a product rule for exponents to simplify each expression.$$(3 b)^{3}$$
Use the power of a product rule for exponents to simplify each expression.$$(5 y)^{4}$$
Use the power of a product rule for exponents to simplify each expression.$$(4 t)^{4}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(3 a^{4} b^{7}\right)^{3}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(5 m^{9} n^{10}\right)^{2}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(-2 r^{2} s^{3}\right)^{3}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(-2 x^{2} y^{4}\right)^{5}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(2 c^{3}\right)^{3}\left(3 c^{4}\right)^{2}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(5 b^{4}\right)^{2}\left(3 b^{8}\right)^{2}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(10 d^{7}\right)^{2}\left(4 d^{9}\right)^{3}$$
Use the power of a product rule for exponents to simplify each expression.$$\left(2 x^{7}\right)^{3}\left(4 x^{8}\right)^{2}$$
Simplify each expression.$$\left(7 a^{9}\right)^{2}$$
Simplify each expression.$$\left(12 b^{6}\right)^{2}$$
Simplify each expression.$$t^{4} \cdot t^{5} \cdot t$$
Simplify each expression.$$n^{4} \cdot n \cdot n^{3}$$
Simplify each expression.$$y^{3} y^{2} y^{4}$$
Simplify each expression.$$y^{4} y y^{6}$$
$$\left(-6 a^{3} b^{2}\right)^{3}$$
Simplify each expression.$$\left(-10 r^{3} s^{2}\right)^{2}$$
Simplify each expression.$$\left(n^{4} n\right)^{3}\left(n^{3}\right)^{6}$$
Simplify each expression.$$\left(y^{3} y\right)^{2}\left(y^{2}\right)^{2}$$
Simplify each expression.$$\left(b^{2} b^{3}\right)^{12}$$
Simplify each expression.$$\left(s^{3} s^{3}\right)^{3}$$
Simplify each expression.$$\left(2 b^{4} b\right)^{5}(3 b)^{2}$$
Simplify each expression.$$\left(2 a a^{7}\right)^{3}(3 a)^{3}$$
Simplify each expression.$$\left(c^{2}\right)^{3}\left(c^{4}\right)^{2}$$
Simplify each expression.$$\left(t^{5}\right)^{2}\left(t^{3}\right)^{3}$$
Simplify each expression.$$\left(3 s^{4} t^{3}\right)^{3}(2 s t)^{4}$$
Simplify each expression.$$\left(2 a^{3} b^{5}\right)^{2}(4 a b)^{3}$$
Simplify each expression.$$x \cdot x^{2} \cdot x^{3} \cdot x^{4} \cdot x^{5}$$
Simplify each expression.$$x^{10} \cdot x^{9} \cdot x^{8} \cdot x^{7}$$
ART HISTORY Leonardo da Vinci's drawing relating a human figure to a square and a circle is shown. Find an expression for the area of the square if the man's height is $5 x$ feet.
PACKAGING Find an expression for the volume of the box shown below.(Figure cannot copy)
Explain the mistake in the following.$$2^{3} \cdot 2^{2}=4^{5}=1,024$$
Explain why we can simplify $x^{4} \cdot x^{5},$ but cannot simplify $x^{4}+x^{5}$.
JEWELRY A lot of what we refer to as gold jewelry is actually made of a combination of gold and another metal. For example, 18 -karat gold is $\frac{18}{24}$ gold by weight. Simplify this ratio.
After evaluation, what is the sign of $(-13)^{5} ?$
\text { Divide: } \frac{-25}{-5}
How much did the temperature change if it went from $-4^{\circ} \mathrm{F}$ to $-17^{\circ} \mathrm{F} ?$
Evaluate: $2\left(\frac{12}{-3}\right)+3(5)$
Solve: $-10=x+1$
Solve: $-x=-12$
Divide: $\frac{0}{10}$
