Simplify h^4(h^3)^-6

$h^{4} {(h^{3})}^{- 6}$

Step 1

Multiply the exponents in ${(h^{3})}^{- 6}$ .

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

$h^{4} h^{3 \cdot - 6}$

Multiply $3$ by $- 6$ .

$h^{4} h^{- 18}$

Step 2

Multiply $h^{4}$ by $h^{- 18}$ by adding the exponents.

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

$h^{4 - 18}$

Subtract $18$ from $4$ .

$h^{- 14}$

Step 3

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

$\frac{1}{h^{14}}$