Checkpoint 2

Correct: B ($3^8$)

Index Law 1: $a^m \times a^n = a^{m+n}$. So $3^5 \times 3^3 = 3^{5+3} = 3^8$.

Correct: B ($2^6$)

Power of a power: $(a^m)^n = a^{mn}$. So $(2^3)^2 = 2^{3 \times 2} = 2^6 = 64$.

Correct: B ($\frac{1}{25}$)

$a^{-n} = \frac{1}{a^n}$. So $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$.

Correct: B ($4.7 \times 10^{-4}$)

Move the decimal 4 places right: $0.00047 = 4.7 \times 10^{-4}$. Coefficient must satisfy $1 \le a < 10$.

Correct: B (4.08)

3 sig figs: the third digit is 7, the next digit is 5, so round up: 4.08.

Correct: A ($8^2$)

Index Law 2: $\frac{a^m}{a^n} = a^{m-n}$. So $\frac{8^5}{8^3} = 8^{5-3} = 8^2 = 64$.

Correct: B (3)

$a^{1/n} = \sqrt[n]{a}$. So $27^{1/3} = \sqrt[3]{27} = 3$.

Correct: A ($4\sqrt{3}$)

$\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$.

Correct: A ($\sqrt{3}$)

$\frac{3}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}$.

Correct: B ($5 \times 10^1$)

$(3 \div 6) \times 10^{4-2} = 0.5 \times 10^2 = 5 \times 10^1$.