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 $\frac{h^{16}}{64}$ .

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

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

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