Algebra Examples

$\frac{{(5 s^{4} q^{- 1})}^{- 4}}{5 s^{- 3} q^{4}}$

Step 1

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

$\frac{1}{5 s^{- 3} q^{4} {(5 s^{4} q^{- 1})}^{4}}$

Step 2

Move $s^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{s^{3}}{5 q^{4} {(5 s^{4} q^{- 1})}^{4}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $5 s^{4} q^{- 1}$ .

$\frac{s^{3}}{5 q^{4} {(5 s^{4})}^{4} {(q^{- 1})}^{4}}$

Step 3.2

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

$\frac{s^{3}}{5 q^{4} (5^{4} {(s^{4})}^{4}) {(q^{- 1})}^{4}}$

Step 3.3

Raise $5$ to the power of $4$ .

$\frac{s^{3}}{5 q^{4} (625 {(s^{4})}^{4}) {(q^{- 1})}^{4}}$

Step 3.4

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

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Step 3.4.1

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

$\frac{s^{3}}{5 q^{4} (625 s^{4 \cdot 4}) {(q^{- 1})}^{4}}$

Step 3.4.2

Multiply $4$ by $4$ .

$\frac{s^{3}}{5 q^{4} (625 s^{16}) {(q^{- 1})}^{4}}$

Step 3.5

Multiply the exponents in ${(q^{- 1})}^{4}$ .

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Step 3.5.1

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

$\frac{s^{3}}{5 q^{4} (625 s^{16}) q^{- 1 \cdot 4}}$

Step 3.5.2

Multiply $- 1$ by $4$ .

$\frac{s^{3}}{5 q^{4} (625 s^{16}) q^{- 4}}$

Step 3.6

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

$\frac{s^{3}}{5 q^{4} \cdot 625 s^{16} \frac{1}{q^{4}}}$

Step 3.7

Combine exponents.

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Step 3.7.1

Multiply $625$ by $5$ .

$\frac{s^{3}}{3125 q^{4} s^{16} \frac{1}{q^{4}}}$

Step 3.7.2

Combine $3125$ and $\frac{1}{q^{4}}$ .

$\frac{s^{3}}{q^{4} s^{16} \frac{3125}{q^{4}}}$

Step 3.7.3

Combine $q^{4}$ and $\frac{3125}{q^{4}}$ .

$\frac{s^{3}}{s^{16} \frac{q^{4} \cdot 3125}{q^{4}}}$

Step 3.7.4

Combine $s^{16}$ and $\frac{q^{4} \cdot 3125}{q^{4}}$ .

$\frac{s^{3}}{\frac{s^{16} (q^{4} \cdot 3125)}{q^{4}}}$

Step 3.8

Remove unnecessary parentheses.

$\frac{s^{3}}{\frac{s^{16} q^{4} \cdot 3125}{q^{4}}}$

Step 3.9

Reduce the expression by cancelling the common factors.

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Step 3.9.1

Reduce the expression $\frac{s^{16} q^{4} \cdot 3125}{q^{4}}$ by cancelling the common factors.

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Step 3.9.1.1

Cancel the common factor.

$\frac{s^{3}}{\frac{s^{16} q^{4} \cdot 3125}{q^{4}}}$

Step 3.9.1.2

Rewrite the expression.

$\frac{s^{3}}{\frac{s^{16} \cdot 3125}{1}}$

Step 3.9.2

Divide $s^{16} \cdot 3125$ by $1$ .

$\frac{s^{3}}{s^{16} \cdot 3125}$

Step 4

Cancel the common factor of $s^{3}$ and $s^{16}$ .

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Step 4.1

Multiply by $1$ .

$\frac{s^{3} \cdot 1}{s^{16} \cdot 3125}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $s^{3}$ out of $s^{16} \cdot 3125$ .

$\frac{s^{3} \cdot 1}{s^{3} (s^{13} \cdot 3125)}$

Step 4.2.2

Cancel the common factor.

$\frac{s^{3} \cdot 1}{s^{3} (s^{13} \cdot 3125)}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{s^{13} \cdot 3125}$

Step 5

Move $3125$ to the left of $s^{13}$ .

$\frac{1}{3125 s^{13}}$