Question

question: *
1 point
which expression is equivalent to ((3x^{2})^{3}(x^{4})^{\frac{1}{2}})?
option 1: (27x^{8})
option 2: (9x^{8})
(27x^{4})
(9x^{4})

Explanation:

Step1: Simplify $(3x^2)^3$

Use power rule: $(ab)^n=a^n b^n$ and $(a^m)^n=a^{mn}$
$(3x^2)^3=3^3 \cdot (x^2)^3=27x^{6}$

Step2: Simplify $(x^4)^{\frac{1}{2}}$

Use power rule: $(a^m)^n=a^{mn}$
$(x^4)^{\frac{1}{2}}=x^{4 \times \frac{1}{2}}=x^2$

Step3: Multiply the two results

Use product rule: $a^m \cdot a^n=a^{m+n}$
$27x^{6} \cdot x^2=27x^{6+2}=27x^8$

Answer:

A. $27x^8$