Name: Zero and negative exponents: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 29 s
Description: Zero and negative exponents: What is the value of 4^-2? Try it, then watch the animated solution.

Start with powers you know:

4^2 = 16

and

4^1 = 4

. Lowering the exponent by

1

divides the value by

4

.

Divide by

4

again:

4^0 = 4 \div 4 = 1

. A zero exponent gives

1

, not

0

.

Keep dividing by

4

:

4^{-1} = \tfrac{1}{4}

, then

4^{-2} = \tfrac{1}{16}

.

The shortcut: a negative exponent means one over the positive power.

4^{-2} = \tfrac{1}{4^2} = \tfrac{1}{16}

.

Traps: a negative exponent never makes the value negative, and

4^2

is

4 \times 4

, not

4 \times 2

.

Try it first