Algebra Examples

$\frac{{(4 x^{- 2} j^{3})}^{- 3}}{3 x^{6} j^{- 4}}$

Step 1

Simplify the expression.

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Step 1.1

Move ${(4 x^{- 2} j^{3})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3 x^{6} j^{- 4} {(4 x^{- 2} j^{3})}^{3}}$

Step 1.2

Move $j^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{j^{4}}{3 x^{6} {(4 x^{- 2} j^{3})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 x^{- 2} j^{3}$ .

$\frac{j^{4}}{3 x^{6} {(4 x^{- 2})}^{3} {(j^{3})}^{3}}$

Step 2.2

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

$\frac{j^{4}}{3 x^{6} {(4 \frac{1}{x^{2}})}^{3} {(j^{3})}^{3}}$

Step 2.3

Combine $4$ and $\frac{1}{x^{2}}$ .

$\frac{j^{4}}{3 x^{6} {(\frac{4}{x^{2}})}^{3} {(j^{3})}^{3}}$

Step 2.4

Apply the product rule to $\frac{4}{x^{2}}$ .

$\frac{j^{4}}{3 x^{6} \frac{4^{3}}{{(x^{2})}^{3}} {(j^{3})}^{3}}$

Step 2.5

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

$\frac{j^{4}}{3 x^{6} \frac{64}{{(x^{2})}^{3}} {(j^{3})}^{3}}$

Step 2.6

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 2.6.1

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

$\frac{j^{4}}{3 x^{6} \frac{64}{x^{2 \cdot 3}} {(j^{3})}^{3}}$

Step 2.6.2

Multiply $2$ by $3$ .

$\frac{j^{4}}{3 x^{6} \frac{64}{x^{6}} {(j^{3})}^{3}}$

Step 2.7

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

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Step 2.7.1

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

$\frac{j^{4}}{3 x^{6} \frac{64}{x^{6}} j^{3 \cdot 3}}$

Step 2.7.2

Multiply $3$ by $3$ .

$\frac{j^{4}}{3 x^{6} \frac{64}{x^{6}} j^{9}}$

Step 2.8

Combine exponents.

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Step 2.8.1

Combine $3$ and $\frac{64}{x^{6}}$ .

$\frac{j^{4}}{x^{6} \frac{3 \cdot 64}{x^{6}} j^{9}}$

Step 2.8.2

Multiply $3$ by $64$ .

$\frac{j^{4}}{x^{6} \frac{192}{x^{6}} j^{9}}$

Step 2.8.3

Combine $x^{6}$ and $\frac{192}{x^{6}}$ .

$\frac{j^{4}}{\frac{x^{6} \cdot 192}{x^{6}} j^{9}}$

Step 2.8.4

Combine $\frac{x^{6} \cdot 192}{x^{6}}$ and $j^{9}$ .

$\frac{j^{4}}{\frac{x^{6} \cdot 192 j^{9}}{x^{6}}}$

Step 2.9

Reduce the expression by cancelling the common factors.

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Step 2.9.1

Reduce the expression $\frac{x^{6} \cdot 192 j^{9}}{x^{6}}$ by cancelling the common factors.

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Step 2.9.1.1

Cancel the common factor.

$\frac{j^{4}}{\frac{x^{6} \cdot 192 j^{9}}{x^{6}}}$

Step 2.9.1.2

Rewrite the expression.

$\frac{j^{4}}{\frac{192 j^{9}}{1}}$

Step 2.9.2

Divide $192 j^{9}$ by $1$ .

$\frac{j^{4}}{192 j^{9}}$

Step 3

Cancel the common factor of $j^{4}$ and $j^{9}$ .

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Step 3.1

Multiply by $1$ .

$\frac{j^{4} \cdot 1}{192 j^{9}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $j^{4}$ out of $192 j^{9}$ .

$\frac{j^{4} \cdot 1}{j^{4} (192 j^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{j^{4} \cdot 1}{j^{4} (192 j^{5})}$

Step 3.2.3

Rewrite the expression.

$\frac{1}{192 j^{5}}$