Question

1. simplify the expression.

$6^{\frac{3}{4}} \cdot 6^{\frac{5}{4}}$
$6^{\frac{3}{4}} \cdot 6^{\frac{5}{4}} = \square$

Explanation:

Step1: Apply exponent product rule

When multiplying two exponents with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, \(a = 6\), \(m=\frac{3}{4}\), and \(n = \frac{5}{4}\). So we calculate \(\frac{3}{4}+\frac{5}{4}\).
\(\frac{3}{4}+\frac{5}{4}=\frac{3 + 5}{4}=\frac{8}{4}=2\)

Step2: Simplify the expression

Now substitute the sum of the exponents back into the base - exponent form. So \(6^{\frac{3}{4}}\cdot6^{\frac{5}{4}}=6^{\frac{3}{4}+\frac{5}{4}}=6^{2}\)
And \(6^{2}=6\times6 = 36\)

Answer:

\(36\)