Introduction to Exponents: Additional Practice (Set 1)

Work out each power, then subtract.

$3^3 = 27, \quad 2^4 = 16, \quad 27 - 16 = 11$

The two powers are evaluated before the subtraction.

In $-5^2$ the exponent attaches only to the $5$, so square first, then apply the minus sign.

$-5^2 = -25, \quad 3^2 = 9, \quad -25 + 9 = -16$

It is not $(-5)^2 = 25$, which would have given $34$.

Evaluate the power, then read its last digit.

$3^4 = 81$

The ones digit is $1$.

Squaring multiplies the fraction by itself.

$\left(\frac{3}{4}\right)^2 = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$

Evaluate the power, then add the two equal values.

$4^2 = 16, \quad 16 + 16 = 32$

It is not $4^4 = 256$; adding two copies doubles the value, it does not add the exponents.

Test each power.

$2^5 = 32, \quad 4^3 = 64, \quad 8^3 = 512, \quad 6^2 = 36$

Only $4^3 = 64$. (Note $2^6$ also equals $64$, but it is not one of the choices.)

Resolve the parentheses first, then square the result.

$2 \times 3 = 6, \quad 6^2 = 36$

Without the parentheses, $2 \times 3^2 = 2 \times 9 = 18$ instead.

Evaluate the numerator and denominator, then divide.

$10^3 = 1000, \quad 5^2 = 25, \quad 1000 \div 25 = 40$

Find a positive number whose cube is $27$.

$3 \times 3 \times 3 = 27$

So $n = 3$.

Power first, then multiplication, then addition.

$2^3 = 8, \quad 3 \times 8 = 24, \quad 1 + 24 = 25$

The area of a square is the side length squared.

$9^2 = 9 \times 9 = 81$

So the area is $81$ square metres. It is not $9 \times 2 = 18$.

Evaluate each power, then subtract.

$2^5 = 32, \quad 3^3 = 27, \quad 32 - 27 = 5$

The two powers are worked out before the subtraction.