Finite Math Examples

${(- 2 w^{- 2} d^{6})}^{2}$

Step 1

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

${(- 2 \frac{1}{w^{2}} d^{6})}^{2}$

Step 2

Combine $- 2$ and $\frac{1}{w^{2}}$ .

${(\frac{- 2}{w^{2}} d^{6})}^{2}$

Step 3

Move the negative in front of the fraction.

${(- \frac{2}{w^{2}} d^{6})}^{2}$

Step 4

Combine $d^{6}$ and $\frac{2}{w^{2}}$ .

${(- \frac{d^{6} \cdot 2}{w^{2}})}^{2}$

Step 5

Move $2$ to the left of $d^{6}$ .

${(- \frac{2 \cdot d^{6}}{w^{2}})}^{2}$

Step 6

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

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Step 6.1

Apply the product rule to $- \frac{2 d^{6}}{w^{2}}$ .

${(- 1)}^{2} {(\frac{2 d^{6}}{w^{2}})}^{2}$

Step 6.2

Apply the product rule to $\frac{2 d^{6}}{w^{2}}$ .

${(- 1)}^{2} \frac{{(2 d^{6})}^{2}}{{(w^{2})}^{2}}$

Step 6.3

Apply the product rule to $2 d^{6}$ .

${(- 1)}^{2} \frac{2^{2} {(d^{6})}^{2}}{{(w^{2})}^{2}}$

Step 7

Simplify the expression.

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Step 7.1

Raise $- 1$ to the power of $2$ .

$1 \frac{2^{2} {(d^{6})}^{2}}{{(w^{2})}^{2}}$

Step 7.2

Multiply $\frac{2^{2} {(d^{6})}^{2}}{{(w^{2})}^{2}}$ by $1$ .

$\frac{2^{2} {(d^{6})}^{2}}{{(w^{2})}^{2}}$

Step 8

Simplify the numerator.

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Step 8.1

Raise $2$ to the power of $2$ .

$\frac{4 {(d^{6})}^{2}}{{(w^{2})}^{2}}$

Step 8.2

Multiply the exponents in ${(d^{6})}^{2}$ .

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Step 8.2.1

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

$\frac{4 d^{6 \cdot 2}}{{(w^{2})}^{2}}$

Step 8.2.2

Multiply $6$ by $2$ .

$\frac{4 d^{12}}{{(w^{2})}^{2}}$

Step 9

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

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Step 9.1

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

$\frac{4 d^{12}}{w^{2 \cdot 2}}$

Step 9.2

Multiply $2$ by $2$ .

$\frac{4 d^{12}}{w^{4}}$