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

Sum the fractions in the exponent.
$4^{\frac{5+5}{4}} = 4^{\frac{10}{4}}$

Step3: Simplify the exponent

Reduce the fraction to lowest terms.
$4^{\frac{5}{2}}$

Step4: Rewrite as radical and simplify

Express the exponent as a root and power: $a^{\frac{m}{n}} = \sqrt[n]{a^m}$
$4^{\frac{5}{2}} = (\sqrt{4})^5 = 2^5$

Step5: Calculate the final power

Compute the value of $2^5$.
$2^5 = 32$

Answer:

32