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 does d^0 equal for any non-zero d?

Back

d^0 = 1.

Front

Simplify: 5x^-2

Back

5/x^2.

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: a^3 * a^-5

Back

a^(3-5) = a^-2 = 1/a^2.

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: (3a^2b^-1)/(6a^-1b^2)

Back

(3/6) * (a^(2-(-1))) * (b^(-1-2)) = 1/2 * a^3 * b^-3 = a^3/(2b^3).

Front

What is the value of (x^0)/(y^0) for any non-zero x and y?

Back

(x^0)/(y^0) = 1/1 = 1.

Front

Simplify: 4^-1

Back

1/4.