Write the Fraction in Simplest Form (-10h^6)/((2h^-3)^5)

$\frac{- 10 h^{6}}{{(2 h^{- 3})}^{5}}$

Step 1

Simplify the denominator.

Apply the product rule to $2 h^{- 3}$ .

$\frac{- 10 h^{6}}{2^{5} {(h^{- 3})}^{5}}$

Raise $2$ to the power of $5$ .

$\frac{- 10 h^{6}}{32 {(h^{- 3})}^{5}}$

Multiply the exponents in ${(h^{- 3})}^{5}$ .

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

$\frac{- 10 h^{6}}{32 h^{- 3 \cdot 5}}$

Multiply $- 3$ by $5$ .

$\frac{- 10 h^{6}}{32 h^{- 15}}$

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

$\frac{- 10 h^{6}}{32 \frac{1}{h^{15}}}$

Step 2

Combine $32$ and $\frac{1}{h^{15}}$ .

$\frac{- 10 h^{6}}{\frac{32}{h^{15}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- 10 h^{6} \frac{h^{15}}{32}$

Step 4

Cancel the common factor of $2$ .

Factor $2$ out of $- 10 h^{6}$ .

$2 (- 5 h^{6}) \frac{h^{15}}{32}$

Factor $2$ out of $32$ .

$2 (- 5 h^{6}) \frac{h^{15}}{2 (16)}$

Cancel the common factor.

$2 (- 5 h^{6}) \frac{h^{15}}{2 \cdot 16}$

Rewrite the expression.

$- 5 h^{6} \frac{h^{15}}{16}$

Step 5

Combine $- 5$ and $\frac{h^{15}}{16}$ .

$h^{6} \frac{- 5 h^{15}}{16}$

Step 6

Combine $h^{6}$ and $\frac{- 5 h^{15}}{16}$ .

$\frac{h^{6} (- 5 h^{15})}{16}$

Step 7

Multiply $h^{6}$ by $h^{15}$ by adding the exponents.

Move $h^{15}$ .

$\frac{h^{15} h^{6} \cdot - 5}{16}$

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

$\frac{h^{15 + 6} \cdot - 5}{16}$

Add $15$ and $6$ .

$\frac{h^{21} \cdot - 5}{16}$

Step 8

Move $- 5$ to the left of $h^{21}$ .

$\frac{- 5 \cdot h^{21}}{16}$

Step 9

Move the negative in front of the fraction.

$- \frac{5 h^{21}}{16}$

Write the Fraction in Simplest Form (-10h^6)/((2h^-3)^5)

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