Exponents

Exponents are a shorthand way of representing repeated multiplication of the same number. The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.

Basic Terminology:

• Base: The number that is being multiplied in the expression. For example, in 2³, 2 is the base.
• Exponent: The number that represents how many times the base is being multiplied. In the expression 2³, 3 is the exponent.
• Power: The result of raising a base to an exponent. In 2³, the power is 8.

Rules of Exponents:

1. Product of Powers: When multiplying two powers with the same base, add the exponents. For example: 2³ * 2⁴ = 2⁷.
2. Quotient of Powers: When dividing two powers with the same base, subtract the exponents. For example: 2⁵ / 2² = 2³.
3. Power of a Power: When raising a power to another power, multiply the exponents. For example: (2³)² = 2⁶.
4. Zero Exponent: Any non-zero number raised to the power of 0 is 1. For example: 5⁰ = 1.
5. Negative Exponent: A negative exponent indicates the reciprocal of the base raised to the positive exponent. For example: 2^-3 = 1/(2³).

Practice Problems:

1. Calculate the value of 4².
2. Simplify the expression 3⁴ * 3².
3. What is 5⁰?
4. Find the value of (2³)².
5. Simplify the expression 6² / 6⁴.
6. Calculate the value of 7^-2.

Answer 1: 4² = 16

Answer 2: 3⁴ * 3² = 3⁶

Answer 3: 5⁰ = 1

Answer 4: (2³)² = 2⁶

Answer 5: 6² / 6⁴ = 1/6² = 1/36

Answer 6: 7^-2 = 1/(7²) = 1/49

[Exponents] Related Worksheets and Study Guides:

• Exponents, Factors and FractionsMathematics • Seventh Grade