Exponents and polynomials | Practice Problems, Examples & Solutions

Exponents and Polynomials

Exponents are a special kind of mathematical expression known as an algebraic expression. Exponents are not a part of the number system; they are a way of writing a number or a variable raised to a power. Exponents can be applied to any constant. Exponents can be put in different orders such as, 2 to the third power to write 2 to the third power. The expression (2 to the third) means the number 2 raised to the third power. Another order is 5 to the second power to write 5 to the second power. The expression (5 to the second) means the number 5 raised to the second power. Exponents are typically used in the following situations: A number raised to a power is written without a limit. For example, the number 2,000 is written as 2 to the first power (2 to the power of 1) and the number 2,000,000 is written as 2 to the second power (2 to the power of 2). The number 2 raised to the second power (2 to the second power) is 22 = 4. The number 28 raised to the third power (27 to the third power) is 2 to the fourth power or 2 to the eighth power (2 to the power of 3) = 720. The number 4,728 raised to the fifth power (4,727 to the fifth power) is 2 to the sixth power or 2 to the fifteenth power (2 to the power of 5) = 1,024,576. The number 22 raised to the third power (22 to the third power) is 22 = 4. The number 1,800 raised to the fourth power (1,799 to the fourth power) is 22 = 8. The number 17 raised to the fourth power (17 to the fourth power) is 22 = 8. The number 1,800 raised to the fourth power (1,799 to the fourth power) is 22 = 8. The number 4,000 raised to the third power (4,000 to the third power) is 28 = 256. The number 16 raised to the fifth power (16 to the fifth power) is 2 to the sixth power or 2 to the fifteenth power (2 to the power of 5) = 1,024,576. The number 5 raised to the seventh power (5 to the seventh power) is 22 = 256. The number 2 raised to the third power is 22 = 4. The number 3 raised to the fourth power is 36 = 9. The number 0.15 raised to the second power is 0.015. The number 0.015 raised to the fourth power is 0.0025. The number 1.5 raised to the third power is 15 = 1. The number 1.5 raised to the second power is 15 = 1. The number 0.0001 raised to the second power is 0.001. The number 0.0001 raised to the fourth power is 0.0001. The number 1 raised to the fourth power is 1. The number 1.33 raised to the fourth power is 1.33 = 0.25. The number 1.33 raised to the third power is 1.33 = 0.25. The number 1.33 raised to the second power is 1.33 = 0.25. The number 0.1 raised to the third power is 0.1 = 1. The number 0.01 raised to the third power is 0.01 = 1. The number 0.01 raised to the second power is 0.01 = 1. The number 0.01 raised to the third power is 0.01 = 1. The number 0.01 raised to the fourth power is 0.01 = 1. The number 0.0001 raised to the third power is 0.0001. The number 0.00001 raised to the third power is 0.000001. The number 4 raised to the second power is 4.

Multiplication Rules for Exponents

419 Practice Problems

01:08

Introductory and Intermediate Algebra for College Students

Multiply and simplify. Assume that all in variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers.
$\sqrt{8 x} \cdot \sqrt{10 y}$

Radicals, Radical Functions, and Rational Exponents

Multiplying and Simplifying Radical Expressions

00:48

Introductory and Intermediate Algebra for College Students

Multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no
radicands involve negative quantities raised to even powers.
$\sqrt{12} \cdot \sqrt{2}$

Radicals, Radical Functions, and Rational Exponents

Multiplying and Simplifying Radical Expressions

01:07

Introductory and Intermediate Algebra for College Students

Simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no
radicands involve negative quantities raised to even powers.
$$\sqrt{x^{7}}$$

Radicals, Radical Functions, and Rational Exponents

Multiplying and Simplifying Radical Expressions