Question

Radicals and Exponents Identify the choice that best completes the question

Answer 1

4)

Given

`(\sqrt[]{2x}-5)(\sqrt[]{2x}+5)`

Simplify as shown below

`\begin{gathered} (\sqrt[]{2x}-5)(\sqrt[]{2x}+5)=\sqrt[]{2x}\cdot\sqrt[]{2x}-5\sqrt[]{2x}+5\sqrt[]{2x}-25 \\ =2x^{}-25 \\ \Rightarrow(\sqrt[]{2x}-5)(\sqrt[]{2x}+5)=2x^{}-25 \end{gathered}`

The answer is 2x-25, option a.

5) Given

`(3x+2)^{(2)/(3)}=(5x-1)^{(1)/(2)}`

Notice that the least common multiple of 2 and 3 is six; thus,

`\begin{gathered} (3x+2)^{(2)/(3)}=(5x-1)^{(1)/(2)} \\ \Rightarrow((3x+2)^{(2)/(3)})^6=((5x-1)^{(1)/(2)})^6 \\ \Rightarrow(3x+2)^{(2)/(3)\cdot6}=(5x-1)^{(1)/(2)\cdot6} \\ \Rightarrow(3x+2)^{(12)/(3)}=(5x-1)^{(6)/(2)} \\ \Rightarrow(3x+2)^4=(5x-1)^3 \end{gathered}`

Therefore, the answer is to raise both sides to the 6th power, option d.