4)
Given
[tex](\sqrt[]{2x}-5)(\sqrt[]{2x}+5)[/tex]
Simplify as shown below
[tex]\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}[/tex]
The answer is 2x-25, option a.
5) Given
[tex](3x+2)^{\frac{2}{3}}=(5x-1)^{\frac{1}{2}}[/tex]
Notice that the least common multiple of 2 and 3 is six; thus,
[tex]\begin{gathered} (3x+2)^{\frac{2}{3}}=(5x-1)^{\frac{1}{2}} \\ \Rightarrow((3x+2)^{\frac{2}{3}})^6=((5x-1)^{\frac{1}{2}})^6 \\ \Rightarrow(3x+2)^{\frac{2}{3}\cdot6}=(5x-1)^{\frac{1}{2}\cdot6} \\ \Rightarrow(3x+2)^{\frac{12}{3}}=(5x-1)^{\frac{6}{2}} \\ \Rightarrow(3x+2)^4=(5x-1)^3 \end{gathered}[/tex]
Therefore, the answer is to raise both sides to the 6th power, option d.
