Algebra Examples

${(3 x^{- 2})}^{4} {(x^{2} y^{4})}^{3}$

Step 1

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

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

Step 2

Combine $3$ and $\frac{1}{x^{2}}$ .

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

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{3}{x^{2}}$ .

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

Step 3.2

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

$\frac{81}{{(x^{2})}^{4}} {(x^{2} y^{4})}^{3}$

Step 3.3

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

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Step 3.3.1

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

$\frac{81}{x^{2 \cdot 4}} {(x^{2} y^{4})}^{3}$

Step 3.3.2

Multiply $2$ by $4$ .

$\frac{81}{x^{8}} {(x^{2} y^{4})}^{3}$

Step 3.4

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

$\frac{81}{x^{8}} ({(x^{2})}^{3} {(y^{4})}^{3})$

Step 3.5

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

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Step 3.5.1

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

$\frac{81}{x^{8}} (x^{2 \cdot 3} {(y^{4})}^{3})$

Step 3.5.2

Multiply $2$ by $3$ .

$\frac{81}{x^{8}} (x^{6} {(y^{4})}^{3})$

Step 4

Cancel the common factor of $x^{6}$ .

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Step 4.1

Factor $x^{6}$ out of $x^{8}$ .

$\frac{81}{x^{6} x^{2}} (x^{6} {(y^{4})}^{3})$

Step 4.2

Factor $x^{6}$ out of $x^{6} {(y^{4})}^{3}$ .

$\frac{81}{x^{6} x^{2}} (x^{6} ({(y^{4})}^{3}))$

Step 4.3

Cancel the common factor.

$\frac{81}{x^{6} x^{2}} (x^{6} {(y^{4})}^{3})$

Step 4.4

Rewrite the expression.

$\frac{81}{x^{2}} {(y^{4})}^{3}$

Step 5

Combine $\frac{81}{x^{2}}$ and ${(y^{4})}^{3}$ .

$\frac{81 {(y^{4})}^{3}}{x^{2}}$

Step 6

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

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Step 6.1

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

$\frac{81 y^{4 \cdot 3}}{x^{2}}$

Step 6.2

Multiply $4$ by $3$ .

$\frac{81 y^{12}}{x^{2}}$