Algebra Examples

${(a^{11} b^{- 10} c d^{- 1})}^{- 2}$

Step 1

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

${(a^{11} \frac{1}{b^{10}} c d^{- 1})}^{- 2}$

Step 2

Combine $a^{11}$ and $\frac{1}{b^{10}}$ .

${(\frac{a^{11}}{b^{10}} c d^{- 1})}^{- 2}$

Step 3

Combine $\frac{a^{11}}{b^{10}}$ and $c$ .

${(\frac{a^{11} c}{b^{10}} d^{- 1})}^{- 2}$

Step 4

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

${(\frac{a^{11} c}{b^{10}} \cdot \frac{1}{d})}^{- 2}$

Step 5

Combine.

${(\frac{a^{11} c \cdot 1}{b^{10} d})}^{- 2}$

Step 6

Multiply $a^{11}$ by $1$ .

${(\frac{a^{11} c}{b^{10} d})}^{- 2}$

Step 7

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

${(\frac{b^{10} d}{a^{11} c})}^{2}$

Step 8

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

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Step 8.1

Apply the product rule to $\frac{b^{10} d}{a^{11} c}$ .

$\frac{{(b^{10} d)}^{2}}{{(a^{11} c)}^{2}}$

Step 8.2

Apply the product rule to $b^{10} d$ .

$\frac{{(b^{10})}^{2} d^{2}}{{(a^{11} c)}^{2}}$

Step 8.3

Apply the product rule to $a^{11} c$ .

$\frac{{(b^{10})}^{2} d^{2}}{{(a^{11})}^{2} c^{2}}$

Step 9

Multiply the exponents in ${(b^{10})}^{2}$ .

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Step 9.1

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

$\frac{b^{10 \cdot 2} d^{2}}{{(a^{11})}^{2} c^{2}}$

Step 9.2

Multiply $10$ by $2$ .

$\frac{b^{20} d^{2}}{{(a^{11})}^{2} c^{2}}$

Step 10

Multiply the exponents in ${(a^{11})}^{2}$ .

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Step 10.1

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

$\frac{b^{20} d^{2}}{a^{11 \cdot 2} c^{2}}$

Step 10.2

Multiply $11$ by $2$ .

$\frac{b^{20} d^{2}}{a^{22} c^{2}}$