Algebra Examples

$\frac{{(5 h^{- 5} s^{- 4})}^{- 3}}{20 h^{5} s^{- 7}}$

Step 1

Move ${(5 h^{- 5} s^{- 4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{20 h^{5} s^{- 7} {(5 h^{- 5} s^{- 4})}^{3}}$

Step 2

Move $s^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{s^{7}}{20 h^{5} {(5 h^{- 5} s^{- 4})}^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

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

$\frac{s^{7}}{20 h^{5} {(5 h^{- 5})}^{3} {(s^{- 4})}^{3}}$

Step 3.2

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

$\frac{s^{7}}{20 h^{5} {(5 \frac{1}{h^{5}})}^{3} {(s^{- 4})}^{3}}$

Step 3.3

Combine $5$ and $\frac{1}{h^{5}}$ .

$\frac{s^{7}}{20 h^{5} {(\frac{5}{h^{5}})}^{3} {(s^{- 4})}^{3}}$

Step 3.4

Apply the product rule to $\frac{5}{h^{5}}$ .

$\frac{s^{7}}{20 h^{5} \frac{5^{3}}{{(h^{5})}^{3}} {(s^{- 4})}^{3}}$

Step 3.5

Raise $5$ to the power of $3$ .

$\frac{s^{7}}{20 h^{5} \frac{125}{{(h^{5})}^{3}} {(s^{- 4})}^{3}}$

Step 3.6

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

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Step 3.6.1

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

$\frac{s^{7}}{20 h^{5} \frac{125}{h^{5 \cdot 3}} {(s^{- 4})}^{3}}$

Step 3.6.2

Multiply $5$ by $3$ .

$\frac{s^{7}}{20 h^{5} \frac{125}{h^{15}} {(s^{- 4})}^{3}}$

Step 3.7

Multiply the exponents in ${(s^{- 4})}^{3}$ .

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Step 3.7.1

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

$\frac{s^{7}}{20 h^{5} \frac{125}{h^{15}} s^{- 4 \cdot 3}}$

Step 3.7.2

Multiply $- 4$ by $3$ .

$\frac{s^{7}}{20 h^{5} \frac{125}{h^{15}} s^{- 12}}$

Step 3.8

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

$\frac{s^{7}}{20 h^{5} \frac{125}{h^{15}} \frac{1}{s^{12}}}$

Step 3.9

Combine exponents.

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Step 3.9.1

Combine $20$ and $\frac{125}{h^{15}}$ .

$\frac{s^{7}}{h^{5} \frac{20 \cdot 125}{h^{15}} \frac{1}{s^{12}}}$

Step 3.9.2

Multiply $20$ by $125$ .

$\frac{s^{7}}{h^{5} \frac{2500}{h^{15}} \frac{1}{s^{12}}}$

Step 3.9.3

Combine $h^{5}$ and $\frac{2500}{h^{15}}$ .

$\frac{s^{7}}{\frac{h^{5} \cdot 2500}{h^{15}} \cdot \frac{1}{s^{12}}}$

Step 3.9.4

Multiply $\frac{h^{5} \cdot 2500}{h^{15}}$ by $\frac{1}{s^{12}}$ .

$\frac{s^{7}}{\frac{h^{5} \cdot 2500}{h^{15} s^{12}}}$

Step 3.10

Reduce the expression $\frac{h^{5} \cdot 2500}{h^{15} s^{12}}$ by cancelling the common factors.

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Step 3.10.1

Factor $h^{5}$ out of $h^{5} \cdot 2500$ .

$\frac{s^{7}}{\frac{h^{5} (2500)}{h^{15} s^{12}}}$

Step 3.10.2

Factor $h^{5}$ out of $h^{15} s^{12}$ .

$\frac{s^{7}}{\frac{h^{5} (2500)}{h^{5} (h^{10} s^{12})}}$

Step 3.10.3

Cancel the common factor.

$\frac{s^{7}}{\frac{h^{5} \cdot 2500}{h^{5} (h^{10} s^{12})}}$

Step 3.10.4

Rewrite the expression.

$\frac{s^{7}}{\frac{2500}{h^{10} s^{12}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$s^{7} \frac{h^{10} s^{12}}{2500}$

Step 5

Multiply $s^{7} \frac{h^{10} s^{12}}{2500}$ .

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Step 5.1

Combine $s^{7}$ and $\frac{h^{10} s^{12}}{2500}$ .

$\frac{s^{7} (h^{10} s^{12})}{2500}$

Step 5.2

Multiply $s^{7}$ by $s^{12}$ by adding the exponents.

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Step 5.2.1

Move $s^{12}$ .

$\frac{s^{12} s^{7} h^{10}}{2500}$

Step 5.2.2

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

$\frac{s^{12 + 7} h^{10}}{2500}$

Step 5.2.3

Add $12$ and $7$ .

$\frac{s^{19} h^{10}}{2500}$