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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Problem
We need to evaluate the expression $$\left(8\right)^{5/3}$$.
This involves raising 8 to the power of \frac{5}{3}.
Step 3:: Rewrite the Base
First, let's recognize that 8 can be written as $$2^{3}$$:
\left(8\right)^{5 / 3} = \left(2^{3}\right)^{5 / 3}
Step 4:: Apply Exponent Rules
Using the power rule $$\left(a^{b}\right)^{c} = a^{bc}$$, we can simplify:
\left(2^{3}\right)^{5 / 3} = 2^{3 \cdot \frac{5}{3}}
Step 5:: Multiply the Exponents
2^{3 \cdot \frac{5}{3}} = 2^{5}
Step 6:: Calculate the Final Value
2^{5} = 32
Final Answer
\left(8\right)^{5 / 3} = 32
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