Question

Simplify the expression. Assume that all variables are positive. Exponents in simplified form should all be
positive.

Answer 1

Given:

The given expression is $\frac{7^{\frac{1}{2}} \cdot 7^{\frac{3}{2}}}{7^{-3}}$

We need to determine the exponents in simplified form.

Exponents in simplified form:

Let us determine the exponent in simplified form.

Let us apply the exponent rule $\frac{x^{a}}{x^{b}}=x^{a-b}$

Thus, we have;

$7^{\frac{1}{2}+\frac{3}{2}-(-3)}$

Adding the fractions, we get;

$7^{\frac{4}{2}-(-3)}$

Cancelling the common terms, we have;

$7^{2-(-3)}$

Simplifying the exponent, we get;

$7^{2+3}$

Adding the exponent, we have;

$7^5$

Thus, the simplified form of the expression is $7^5$