Question

Select the correct answer. Which expression is equivalent to 7x2/204 . 6/2x12, if x0? O A 26.22 O B. 13 r12/2 O C. 84r10 O D 42.r122

Answer 1

We would like to find an equivalent expression for

$7x^2\sqrt[]{2x^4}\cdot6\sqrt[]{2x^{12}}$

To do this, first we have to remember the following rule

$\sqrt[]{a}\sqrt[]{b}=\sqrt[]{ab}$

Then

$\begin{gathered} 7x^2\sqrt[]{2x^4}\cdot6\sqrt[]{2x^{12}}=(7x^2)(6)(\sqrt[]{2x^4})(\sqrt[]{2x^{12})} \\ =42x^2\sqrt[]{(2x^4)(2x^{12})} \\ =42x^2\sqrt[]{4x^{16}} \end{gathered}$

To simplify the squared root we have to remember yet another rule

$(a^m)^n=a^{mn}$

Hence

$\begin{gathered} 7x^2\sqrt[]{2x^4}\cdot6\sqrt[]{2x^2}=42x^2\sqrt[]{(2x^8)^2} \\ =42x^2\cdot2x^8 \\ =84x^{10} \end{gathered}$

Therefore the answer is C.