Question

simplify the following expression using only positive exponents

Answer 1

Given:

The given expression is $x^{\frac{3}{4}} \cdot x^{\frac{5}{3}}$

We need to simplify the given expression.

Simplification:

Let us simplify the expression using positive exponents.

Let us apply the exponent rule, $a^{b} \cdot a^{c}=a^{b+c}$

Thus, we have;

$x^{\frac{3}{4}} x^{\frac{5}{3}}=x^{\frac{3}{4}+\frac{5}{3}}$

Let us simplify the exponent by taking LCM.

Thus, we get;

$x^{\frac{3}{4}} x^{\frac{5}{3}}=x^{\frac{9+20}{12}}$

Simplifying, we get;

$x^{\frac{3}{4}} x^{\frac{5}{3}}=x^{\frac{29}{12}}$

Thus, the simplified value of the given expression is $x^{\frac{29}{12}}$

Hence, Option c is the correct answer.