Algebra Examples

$\frac{{(4 s^{- 1} j^{- 3})}^{- 3}}{20 s^{- 2}}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{1}{20 s^{- 2} {(4 s^{- 1} j^{- 3})}^{3}}$

Step 1.2

Move $s^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{s^{2}}{20 {(4 s^{- 1} j^{- 3})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{s^{2}}{20 {(4 s^{- 1})}^{3} {(j^{- 3})}^{3}}$

Step 2.2

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

$\frac{s^{2}}{20 {(4 \frac{1}{s})}^{3} {(j^{- 3})}^{3}}$

Step 2.3

Combine $4$ and $\frac{1}{s}$ .

$\frac{s^{2}}{20 {(\frac{4}{s})}^{3} {(j^{- 3})}^{3}}$

Step 2.4

Apply the product rule to $\frac{4}{s}$ .

$\frac{s^{2}}{20 \frac{4^{3}}{s^{3}} {(j^{- 3})}^{3}}$

Step 2.5

Raise $4$ to the power of $3$ .

$\frac{s^{2}}{20 \frac{64}{s^{3}} {(j^{- 3})}^{3}}$

Step 2.6

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

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Step 2.6.1

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

$\frac{s^{2}}{20 \frac{64}{s^{3}} j^{- 3 \cdot 3}}$

Step 2.6.2

Multiply $- 3$ by $3$ .

$\frac{s^{2}}{20 \frac{64}{s^{3}} j^{- 9}}$

Step 2.7

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

$\frac{s^{2}}{20 \frac{64}{s^{3}} \frac{1}{j^{9}}}$

Step 2.8

Combine exponents.

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Step 2.8.1

Combine $20$ and $\frac{64}{s^{3}}$ .

$\frac{s^{2}}{\frac{20 \cdot 64}{s^{3}} \cdot \frac{1}{j^{9}}}$

Step 2.8.2

Multiply $20$ by $64$ .

$\frac{s^{2}}{\frac{1280}{s^{3}} \cdot \frac{1}{j^{9}}}$

Step 2.8.3

Multiply $\frac{1280}{s^{3}}$ by $\frac{1}{j^{9}}$ .

$\frac{s^{2}}{\frac{1280}{s^{3} j^{9}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$s^{2} \frac{s^{3} j^{9}}{1280}$

Step 4

Multiply $s^{2} \frac{s^{3} j^{9}}{1280}$ .

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Step 4.1

Combine $s^{2}$ and $\frac{s^{3} j^{9}}{1280}$ .

$\frac{s^{2} (s^{3} j^{9})}{1280}$

Step 4.2

Multiply $s^{2}$ by $s^{3}$ by adding the exponents.

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Step 4.2.1

Move $s^{3}$ .

$\frac{s^{3} s^{2} j^{9}}{1280}$

Step 4.2.2

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

$\frac{s^{3 + 2} j^{9}}{1280}$

Step 4.2.3

Add $3$ and $2$ .

$\frac{s^{5} j^{9}}{1280}$