Simplify (-12h^-4)/((4h^-5)^4)

$\frac{- 12 h^{- 4}}{{(4 h^{- 5})}^{4}}$

Step 1

Move $h^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 12}{{(4 h^{- 5})}^{4} h^{4}}$

Step 2

Simplify the denominator.

Apply the product rule to $4 h^{- 5}$ .

$\frac{- 12}{4^{4} {(h^{- 5})}^{4} h^{4}}$

Raise $4$ to the power of $4$ .

$\frac{- 12}{256 {(h^{- 5})}^{4} h^{4}}$

Multiply the exponents in ${(h^{- 5})}^{4}$ .

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

$\frac{- 12}{256 h^{- 5 \cdot 4} h^{4}}$

Multiply $- 5$ by $4$ .

$\frac{- 12}{256 h^{- 20} h^{4}}$

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

$\frac{- 12}{256 \frac{1}{h^{20}} h^{4}}$

Combine exponents.

Combine $256$ and $\frac{1}{h^{20}}$ .

$\frac{- 12}{\frac{256}{h^{20}} h^{4}}$

Combine $\frac{256}{h^{20}}$ and $h^{4}$ .

$\frac{- 12}{\frac{256 h^{4}}{h^{20}}}$

Reduce the expression $\frac{256 h^{4}}{h^{20}}$ by cancelling the common factors.

Factor $h^{4}$ out of $256 h^{4}$ .

$\frac{- 12}{\frac{h^{4} \cdot 256}{h^{20}}}$

Factor $h^{4}$ out of $h^{20}$ .

$\frac{- 12}{\frac{h^{4} \cdot 256}{h^{4} h^{16}}}$

Cancel the common factor.

$\frac{- 12}{\frac{h^{4} \cdot 256}{h^{4} h^{16}}}$

Rewrite the expression.

$\frac{- 12}{\frac{256}{h^{16}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- 12 \frac{h^{16}}{256}$

Step 4

Cancel the common factor of $4$ .

Factor $4$ out of $- 12$ .

$4 (- 3) \frac{h^{16}}{256}$

Factor $4$ out of $256$ .

$4 \cdot - 3 \frac{h^{16}}{4 \cdot 64}$

Cancel the common factor.

$4 \cdot - 3 \frac{h^{16}}{4 \cdot 64}$

Rewrite the expression.

$- 3 \frac{h^{16}}{64}$

Step 5

Combine $- 3$ and $\frac{h^{16}}{64}$ .

$\frac{- 3 h^{16}}{64}$

Step 6

Move the negative in front of the fraction.

$- \frac{3 h^{16}}{64}$

Simplify (-12h^-4)/((4h^-5)^4)

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