Question

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

Explanation:

Step1: Rewrite 125 as power of 5

$125 = 5^3$, so $125^{\frac{3}{4}} = (5^3)^{\frac{3}{4}}$

Step2: Simplify the exponent

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

Step3: Combine the two terms

Use $a^m \cdot a^n = a^{m+n}$:
$5^{\frac{9}{4}} \cdot 5^{\frac{3}{4}} = 5^{\frac{9}{4} + \frac{3}{4}}$

Step4: Add the exponents

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

Step5: Calculate the final value

$5^3 = 5 \times 5 \times 5 = 125$

Answer:

125