Question

simplify.
$5^{\frac{3}{4}} \cdot 125^{\frac{3}{4}}$

Explanation:

Step1: Rewrite 125 as power of 5

$125 = 5^3$

Step2: Substitute into original expression

$5^{\frac{3}{4}} \cdot (5^3)^{\frac{3}{4}}$

Step3: Simplify the exponent term

$(5^3)^{\frac{3}{4}} = 5^{3 \times \frac{3}{4}} = 5^{\frac{9}{4}}$

Step4: Add exponents for same base

$5^{\frac{3}{4} + \frac{9}{4}} = 5^{\frac{12}{4}}$

Step5: Simplify the final exponent

$5^{\frac{12}{4}} = 5^3$

Step6: Calculate the final value

$5^3 = 125$

Answer:

125