Rules of Exponents

Front

What is the rule for negative exponents?

Back

A negative exponent indicates that the base should be taken as the reciprocal. For example, a^(-n) = 1/(a^n).

Front

Simplify: 9^-3

Back

1/9^3

Front

What is the product of powers rule?

Back

When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

Simplify: (-4r^5)(2r^8)

Back

-8r^13

Front

What is the quotient of powers rule?

Back

When dividing two powers with the same base, subtract the exponents: a^m / a^n = a^(m-n).

Front

Evaluate: 9^5 / 9^0

Back

9^5 (since any number to the power of 0 is 1).

Front

What is the zero exponent rule?

Back

Any non-zero number raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

Simplify: (-1/2)^0

Back

1

Front

What is the power of a power rule?

Back

When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).

Front

Simplify: (x^3)(x^4)

Back

x^7 (using the product of powers rule).