Algebra Examples

$\frac{{(- 3 s^{- 1} c^{- 4})}^{2}}{4 s^{10} c^{- 10}}$

Step 1

Move $c^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(- 3 s^{- 1} c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $- 3 s^{- 1} c^{- 4}$ .

$\frac{{(- 3 s^{- 1})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.2

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

$\frac{{(- 3 \frac{1}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.3

Combine $- 3$ and $\frac{1}{s}$ .

$\frac{{(\frac{- 3}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.4

Move the negative in front of the fraction.

$\frac{{(- \frac{3}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.5.1

Apply the product rule to $- \frac{3}{s}$ .

$\frac{{(- 1)}^{2} {(\frac{3}{s})}^{2} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.5.2

Apply the product rule to $\frac{3}{s}$ .

$\frac{{(- 1)}^{2} \frac{3^{2}}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.6

Raise $- 1$ to the power of $2$ .

$\frac{1 \frac{3^{2}}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.7

Multiply $\frac{3^{2}}{s^{2}}$ by $1$ .

$\frac{\frac{3^{2}}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.8

Raise $3$ to the power of $2$ .

$\frac{\frac{9}{s^{2}} {(c^{- 4})}^{2} c^{10}}{4 s^{10}}$

Step 2.9

Multiply the exponents in ${(c^{- 4})}^{2}$ .

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Step 2.9.1

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

$\frac{\frac{9}{s^{2}} c^{- 4 \cdot 2} c^{10}}{4 s^{10}}$

Step 2.9.2

Multiply $- 4$ by $2$ .

$\frac{\frac{9}{s^{2}} c^{- 8} c^{10}}{4 s^{10}}$

Step 2.10

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

$\frac{\frac{9}{s^{2}} \cdot \frac{1}{c^{8}} c^{10}}{4 s^{10}}$

Step 2.11

Combine exponents.

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Step 2.11.1

Multiply $\frac{9}{s^{2}}$ by $\frac{1}{c^{8}}$ .

$\frac{\frac{9}{s^{2} c^{8}} c^{10}}{4 s^{10}}$

Step 2.11.2

Combine $\frac{9}{s^{2} c^{8}}$ and $c^{10}$ .

$\frac{\frac{9 c^{10}}{s^{2} c^{8}}}{4 s^{10}}$

Step 2.12

Reduce the expression $\frac{9 c^{10}}{s^{2} c^{8}}$ by cancelling the common factors.

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Step 2.12.1

Factor $c^{8}$ out of $9 c^{10}$ .

$\frac{\frac{c^{8} (9 c^{2})}{s^{2} c^{8}}}{4 s^{10}}$

Step 2.12.2

Factor $c^{8}$ out of $s^{2} c^{8}$ .

$\frac{\frac{c^{8} (9 c^{2})}{c^{8} s^{2}}}{4 s^{10}}$

Step 2.12.3

Cancel the common factor.

$\frac{\frac{c^{8} (9 c^{2})}{c^{8} s^{2}}}{4 s^{10}}$

Step 2.12.4

Rewrite the expression.

$\frac{\frac{9 c^{2}}{s^{2}}}{4 s^{10}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{9 c^{2}}{s^{2}} \cdot \frac{1}{4 s^{10}}$

Step 4

Combine.

$\frac{9 c^{2} \cdot 1}{s^{2} (4 s^{10})}$

Step 5

Multiply $s^{2}$ by $s^{10}$ by adding the exponents.

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Step 5.1

Move $s^{10}$ .

$\frac{9 c^{2} \cdot 1}{s^{10} s^{2} \cdot 4}$

Step 5.2

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

$\frac{9 c^{2} \cdot 1}{s^{10 + 2} \cdot 4}$

Step 5.3

Add $10$ and $2$ .

$\frac{9 c^{2} \cdot 1}{s^{12} \cdot 4}$

Step 6

Multiply $9 c^{2}$ by $1$ .

$\frac{9 c^{2}}{s^{12} \cdot 4}$

Step 7

Move $4$ to the left of $s^{12}$ .

$\frac{9 c^{2}}{4 s^{12}}$