Negative and Zero Exponents: Practice

Any nonzero base raised to the power $0$ equals $1$.

$5^0 = 1$

A zero exponent means no factors of the base, and a product of no factors is $1$, not $0$.

Take the reciprocal of the positive power $2^2$.

$2^{-2} = \frac{1}{2^2} = \frac{1}{4}$

The answer is positive $\tfrac{1}{4}$, not $-4$: the exponent's sign does not make the value negative.

A negative exponent is one over the positive power.

$2^{-3} = \frac{1}{2^3} = \frac{1}{8}$

It is $\tfrac{1}{8}$, not $\tfrac{1}{6}$: the exponent is repeated multiplication, so $2^3 = 8$, not $2 \times 3 = 6$.

Any nonzero base to the power $0$ is $1$.

$100^0 = 1$

A negative exponent gives the reciprocal of the positive power.

$3^{-1} = \frac{1}{3^1} = \frac{1}{3}$

Take the reciprocal of $3^2$.

$3^{-2} = \frac{1}{3^2} = \frac{1}{9}$

The value is a positive fraction, not $-9$.

One over a power equals that base carrying a negative exponent.

$\frac{1}{5^2} = 5^{-2}$

The base stays $5$; only the exponent's sign changes.

A negative exponent gives the reciprocal of the positive power.

$10^{-1} = \frac{1}{10^1} = \frac{1}{10}$

A zero exponent on a nonzero base equals $1$.

$8^0 = 1$

It is not the base itself, and it is not $0$.

Take the reciprocal of $5^2$.

$5^{-2} = \frac{1}{5^2} = \frac{1}{25}$

It is $\tfrac{1}{25}$, not $\tfrac{1}{10}$: square the $5$, do not multiply $5 \times 2$.

A negative exponent moves the power to the denominator.

$x^{-3} = \frac{1}{x^3}$

A negative exponent is the reciprocal of the positive power.

$4^{-1} = \frac{1}{4^1} = \frac{1}{4}$