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.