Introduction to Exponents: Practice

The exponent $3$ means three factors of $2$ multiplied together.

$2^3 = 2 \times 2 \times 2 = 8$

It is not $2 \times 3 = 6$; the exponent counts the copies, it is not a factor itself.

The base is the number being multiplied repeatedly; the exponent sits above it and counts the copies.

$7^4 = \underbrace{7 \times 7 \times 7 \times 7}_{\text{base } 7}$

So the base is $7$, and the $4$ is the exponent.

Squaring multiplies the base by itself.

$5^2 = 5 \times 5 = 25$

This is read "five squared."

A square is two factors of the base.

$3^2 = 3 \times 3 = 9$

The exponent $3$ means three factors of $10$.

$10^3 = 10 \times 10 \times 10 = 1000$

That is a $1$ followed by three zeros, matching the exponent.

Any number to the first power is just itself, a single copy of the base.

$4^1 = 4$

Four copies of the base $3$ multiplied together is a power with base $3$ and exponent $4$.

$3 \times 3 \times 3 \times 3 = 3^4$

Here $4^3$ would be three copies of $4$, and $3 + 3 + 3 + 3$ is repeated addition, not multiplication.

The exponent $4$ means four factors of $2$, multiplied step by step.

$2^4 = 2 \times 2 \times 2 \times 2 = 16$

The exponent $3$ means three factors of $3$.

$3^3 = 3 \times 3 \times 3 = 27$

This is read "three cubed."

There are four $2$'s multiplied together.

$2 \times 2 \times 2 \times 2 = 2^4$

The base is $2$, and the count of factors, $4$, is the exponent.

The exponent $5$ means five factors of $2$.

$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$

A square is two factors of the base.

$7^2 = 7 \times 7 = 49$