Introduction to Exponents: Practice

Powers come before addition in the order of operations.

$3^2 = 9, \qquad 2 + 9 = 11$

It is not $5^2 = 25$; the addition waits until after the power.

Parentheses are resolved before the exponent.

$2 + 3 = 5, \qquad 5^2 = 25$

Compare with $2 + 3^2 = 11$, where there are no parentheses.

Evaluate the power before multiplying.

$2^3 = 8, \qquad 5 \times 8 = 40$

It is not $(5 \times 2)^3 = 1000$; the exponent attaches only to the $2$.

Evaluate each power, then add the results.

$2^3 = 8, \quad 2^2 = 4, \quad 8 + 4 = 12$

You cannot add the exponents here; each power is worked out on its own first.

A power of ten is a $1$ followed by as many zeros as the exponent.

$10^4 = 10{,}000$

That is a $1$ followed by four zeros.

Evaluate each power first, then subtract.

$4^2 = 16, \quad 3^2 = 9, \quad 16 - 9 = 7$

It is not $(4 - 3)^2 = 1$; subtract the values, not the bases.

Power first, then multiplication, then addition.

$3^2 = 9, \quad 2 \times 9 = 18, \quad 1 + 18 = 19$

The exponent acts only on the $3$, before the $\times$ or the $+$.

The exponent $3$ means three factors of $4$.

$4^3 = 4 \times 4 \times 4 = 64$

Evaluate the power before multiplying.

$10^2 = 100, \qquad 3 \times 100 = 300$

It is not $(3 \times 10)^2 = 900$; the exponent attaches only to the $10$.

Evaluate each power, then add.

$5^2 = 25, \quad 1^7 = 1, \quad 25 + 1 = 26$

Any power of $1$ is $1$.

There are four $5$'s multiplied together, so the base is $5$ and the exponent is $4$.

$5^4 = 5 \times 5 \times 5 \times 5 = 625$

Multiply five factors, each equal to $-1$.

$(-1)^5 = (-1)(-1)(-1)(-1)(-1) = -1$

An odd number of $-1$ factors leaves the product negative; an even number would give $+1$.