Negative Exponents

Front

What is a negative exponent?

Back

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

Front

Simplify: 2^(-3)

Back

1/(2^3) = 1/8.

Front

What is the rule for multiplying powers with the same base?

Back

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

Front

Simplify: x^(-2) * x^3

Back

x^(3-2) = x^1 = x.

Front

What is the rule for dividing powers with the same base?

Back

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

Front

Simplify: (3^(-2))/(3^(-5))

Back

3^(-2 - (-5)) = 3^(3) = 27.

Front

What happens when you raise a power to a negative exponent?

Back

a^(-n) = 1/(a^n).

Front

Simplify: (5^2)^(-1)

Back

1/(5^2) = 1/25.

Front

What is the value of 10^(-1)?

Back

1/10.

Front

If a^(-m) = 1/b, what is b in terms of a and m?

Back

b = a^m.