Algebra Examples

${(\frac{a^{2} b c^{4}}{a^{3} c^{2}})}^{- 2}$

Step 1

Cancel the common factor of $a^{2}$ and $a^{3}$ .

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Step 1.1

Factor $a^{2}$ out of $a^{2} b c^{4}$ .

${(\frac{a^{2} (b c^{4})}{a^{3} c^{2}})}^{- 2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $a^{2}$ out of $a^{3} c^{2}$ .

${(\frac{a^{2} (b c^{4})}{a^{2} (a c^{2})})}^{- 2}$

Step 1.2.2

Cancel the common factor.

${(\frac{a^{2} (b c^{4})}{a^{2} (a c^{2})})}^{- 2}$

Step 1.2.3

Rewrite the expression.

${(\frac{b c^{4}}{a c^{2}})}^{- 2}$

Step 2

Cancel the common factor of $c^{4}$ and $c^{2}$ .

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Step 2.1

Factor $c^{2}$ out of $b c^{4}$ .

${(\frac{c^{2} (b c^{2})}{a c^{2}})}^{- 2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $c^{2}$ out of $a c^{2}$ .

${(\frac{c^{2} (b c^{2})}{c^{2} a})}^{- 2}$

Step 2.2.2

Cancel the common factor.

${(\frac{c^{2} (b c^{2})}{c^{2} a})}^{- 2}$

Step 2.2.3

Rewrite the expression.

${(\frac{b c^{2}}{a})}^{- 2}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{a}{b c^{2}})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{a}{b c^{2}}$ .

$\frac{a^{2}}{{(b c^{2})}^{2}}$

Step 4.2

Apply the product rule to $b c^{2}$ .

$\frac{a^{2}}{b^{2} {(c^{2})}^{2}}$

Step 5

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

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Step 5.1

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

$\frac{a^{2}}{b^{2} c^{2 \cdot 2}}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{a^{2}}{b^{2} c^{4}}$