Question

progress xx
1 evaluate $(-2x^{2})^{3}$
2 evaluate $(-3x^{3})^{3}$
3 evaluate $(3x^{2}y^{7})^{2}$
4 evaluate $(6x^{8}y^{2})^{2}$
answers
a: $-8x^{5}$
b: $-9x^{9}$
c: $-6x^{6}$
d: $9x^{4}y^{14}$
e: $-27x^{6}$
f: $-27x^{9}$
g: $6x^{4}y^{9}$
h: $36x^{10}y^{4}$
i: $12x^{16}y^{4}$
j: $6x^{4}y^{14}$
k: $9x^{4}y^{9}$
l: $36x^{16}y^{4}$
m: $-8x^{6}$
n: $-6x^{5}$
o: $-9x^{6}$

Explanation:

Step1: Apply power rule to $(-2x^2)^3$

Use exponent rule: $(ab)^n=a^n b^n$ and $(a^m)^n=a^{m \cdot n}$

$$\begin{align*} (-2x^2)^3&=(-2)^3 \cdot (x^2)^3\\ &=-8 \cdot x^{2 \times 3}\\ &=-8x^6 \end{align*}$$

Step2: Apply power rule to $(-3x^3)^3$

Use exponent rule: $(ab)^n=a^n b^n$ and $(a^m)^n=a^{m \cdot n}$

$$\begin{align*} (-3x^3)^3&=(-3)^3 \cdot (x^3)^3\\ &=-27 \cdot x^{3 \times 3}\\ &=-27x^9 \end{align*}$$

Step3: Apply power rule to $(3x^2y^7)^2$

Use exponent rule: $(ab)^n=a^n b^n$ and $(a^m)^n=a^{m \cdot n}$

$$\begin{align*} (3x^2y^7)^2&=3^2 \cdot (x^2)^2 \cdot (y^7)^2\\ &=9 \cdot x^{2 \times 2} \cdot y^{7 \times 2}\\ &=9x^4y^{14} \end{align*}$$

Step4: Apply power rule to $(6x^8y^2)^2$

Use exponent rule: $(ab)^n=a^n b^n$ and $(a^m)^n=a^{m \cdot n}$

$$\begin{align*} (6x^8y^2)^2&=6^2 \cdot (x^8)^2 \cdot (y^2)^2\\ &=36 \cdot x^{8 \times 2} \cdot y^{2 \times 2}\\ &=36x^{16}y^4 \end{align*}$$

Answer:

1. M: $-8x^6$
2. F: $-27x^9$
3. D: $9x^4y^{14}$
4. L: $36x^{16}y^4$