Question

simplify.
$243^{\frac{5}{6}} \cdot 3^{\frac{5}{6}}$

Explanation:

Step1: Rewrite 243 as power of 3

$243 = 3^5$

Step2: Substitute into original expression

$3^{5 \cdot \frac{5}{6}} \cdot 3^{\frac{5}{6}}$

Step3: Simplify exponents

$3^{\frac{25}{6}} \cdot 3^{\frac{5}{6}}$

Step4: Add exponents (same base)

$3^{\frac{25}{6} + \frac{5}{6}} = 3^{\frac{30}{6}}$

Step5: Simplify final exponent

$3^5$

Step6: Calculate the result

$3^5 = 243$

Answer:

243