Question

simplify.
\\(4^{\frac{5}{4}}\cdot 4^{\frac{5}{4}}\\)

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$
$4^{\frac{5}{4}} \cdot 4^{\frac{5}{4}} = 4^{\frac{5}{4}+\frac{5}{4}}$

Step2: Add the exponents

$\frac{5}{4}+\frac{5}{4} = \frac{10}{4} = \frac{5}{2}$
So the expression becomes $4^{\frac{5}{2}}$

Step3: Rewrite and simplify the exponent

Rewrite $4$ as $2^2$: $(2^2)^{\frac{5}{2}}$
Apply power rule: $(a^m)^n = a^{m \cdot n}$
$2^{2 \cdot \frac{5}{2}} = 2^5$

Step4: Calculate the final value

$2^5 = 32$

Answer:

32