Simplify (h^-1*h^-5)^(1/2)

${(h^{- 1} \cdot h^{- 5})}^{\frac{1}{2}}$

Step 1

Multiply $h^{- 1}$ by $h^{- 5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(h^{- 1 - 5})}^{\frac{1}{2}}$

Subtract $5$ from $- 1$ .

${(h^{- 6})}^{\frac{1}{2}}$

Step 2

Multiply the exponents in ${(h^{- 6})}^{\frac{1}{2}}$ .

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

$h^{- 6 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

$h^{2 \cdot - 3 \frac{1}{2}}$

Rewrite the expression.

$h^{- 3}$

Step 3

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

$\frac{1}{h^{3}}$