Answers:
5^(3/2)
√(5^3)
Explanation:
We will use the following properties:
[tex]\begin{gathered} 5^a\cdot5^b=5^{a+b} \\ (5^a)^b=5^{a\cdot b} \end{gathered}[/tex]
So, the expression is equivalent to:
[tex](5^{\frac{1}{8}}\cdot5^{\frac{3}{8}})^3=(5^{\frac{1}{8}+\frac{3}{8}})^3[/tex]
Then, 1/8 + 3/8 is equal to:
[tex]\frac{1}{8}+\frac{3}{8}=\frac{1+3}{8}=\frac{4}{8}=\frac{1}{2}[/tex]
So, the expression is:
[tex](5^{\frac{1}{8}+\frac{3}{8}})^3=(5^{\frac{1}{2}})^3=5^{\frac{3}{2}}[/tex]
Additionally, 5^(3/2) is also equal to:
[tex]5^{\frac{3}{2}}=\sqrt[]{5^3}[/tex]
Therefore, the answers are the first and the third option.
