Simplify ((pg^3)^(1/2))/((pg)^(-1/2))

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

Step 1

Multiply the exponents in ${({pg}^{3})}^{\frac{1}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $3$ and $\frac{1}{2}$ .

$\frac{{pg}^{\frac{3}{2}}}{{pg}^{- \frac{1}{2}}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{pg}^{\frac{3}{2}}}{\frac{1}{{pg}^{\frac{1}{2}}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

${pg}^{\frac{3}{2}} {pg}^{\frac{1}{2}}$

Step 4

Combine units.

${pg}^{2}$