Exercise 1b (Oral)

$(a^3)^2$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (a^3)^2=a^{3 \times 2}=a^6$

Answer: $a^6$

$(b^2)^4$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (b^2)^4=a^{2 \times 4}=b^{8}$

Answer: $b^{8}$

$(c^5)^3$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (c^5)^3=c^{5 \times 3}=b^{15}$

Answer: $b^{15}$

$(d^4)^3$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (d^4)^3=d^{4 \times 3}=d^{12}$

Answer: $d^{12}$

$(e^3)^3$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (e^3)^3=e^{3 \times 3}=e^{9}$

Answer: $e^{9}$

$(f^0)^8$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (f^0)^8=f^{0 \times 8}=f^{0}=1$

Answer: $1$

$(g^{-2})^5$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (g^{-2})^5=g^{-2 \times 5}=g^{-10}=\frac{1}{g^{10}}$

Answer: $\frac{1}{g^{10}}$

$(h^4)^{-5}$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (h^4)^{-5}=h^{4 \times -5}=h^{-20}=\frac{1}{h^{20}}$

Answer: $\frac{1}{h^{20}}$

$(5^2)^{-1}$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (5^2)^{-1}=5^{2 \times (-1)}=5^{-2}=\frac{1}{5^2}=\frac{1}{25}$

Answer: $\frac{1}{25}$

$(3^{-2})^{-2}$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (3^{-2})^{-2}=3^{{-2} \times ({-2})}=3^{4}=81$

Answer: $81$

$(10^2)^7$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (10^2)^7=10^{2 \times 7}=10^{14}$

Answer: $10^{14}$

$(2^{-3})^2$

Recall: $(a^m)^n=a^{m \times n}$

$\therefore (2^{-3})^2=2^{{-3} \times 2}=2^{-6}=\frac{1}{2^6}=\frac{1}{64}$

Answer: $\frac{1}{64}$