Introduction to Exponents: Additional Practice (Set 2)

Compute the power, then read its last digit.

$2^{10} = 1024$

The ones (units) digit is $4$.

Count factors of $5$ until you reach $125$.

$5 \times 5 \times 5 = 125$

That is three factors, so $n = 3$.

Count how many factors of $2$ reach $32$.

$2 \times 2 \times 2 \times 2 \times 2 = 32$

That is five factors, so $n = 5$.

Power first, then multiplication, then subtraction.

$4^2 = 16, \quad 16 \times 3 = 48, \quad 50 - 48 = 2$

A power is repeated multiplication, so multiply the fraction by itself three times.

$\left(\frac{2}{3}\right)^3 = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{8}{27}$

Compute each power.

$5^3 = 125, \qquad 3^5 = 243$

So $3^5$ is greater. Swapping the base and exponent changes the value.

Resolve the parentheses, then each power, then add.

$(1 + 2)^2 = 3^2 = 9, \quad 1^2 = 1, \quad 9 + 1 = 10$

Note $(1+2)^2 = 9$ is not $1^2 + 2^2 = 5$; a power does not split over a sum.

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

$(-1)^8 = 1$

An even number of negative factors cancels in pairs to give a positive result, so the value is $1$.

Evaluate both, watching the parentheses.

$(-3)^4 = 81, \qquad -3^4 = -(3^4) = -81$

So $(-3)^4$ is greater: $81$ versus $-81$.

Multiply $0.2$ by itself.

$0.2^2 = 0.2 \times 0.2 = 0.04$

Two tenths times two tenths is four hundredths, not $0.4$.

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

$10^7 = 10{,}000{,}000$

So there are $7$ zeros.

Evaluate the numerator and denominator separately, then divide.

$6^2 - 2^2 = 36 - 4 = 32, \quad 2^3 = 8, \quad 32 \div 8 = 4$