Simplify ((-w^0d)^2)/((-2w^-2d^6)^2)

$\frac{{(- w^{0} d)}^{2}}{{(- 2 w^{- 2} d^{6})}^{2}}$

Step 1

Simplify the numerator.

Apply the product rule to $- w^{0} d$ .

$\frac{{(- w^{0})}^{2} d^{2}}{{(- 2 w^{- 2} d^{6})}^{2}}$

Anything raised to $0$ is $1$ .

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

Multiply $- 1$ by $1$ .

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

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

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

Multiply $d^{2}$ by $1$ .

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

Step 2

Simplify the denominator.

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

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

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

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

Multiply $6$ by $2$ .

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

Step 3

Combine $\frac{4}{w^{4}}$ and $d^{12}$ .

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

Step 4

Multiply the numerator by the reciprocal of the denominator.

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

Step 5

Cancel the common factor of $d^{2}$ .

Factor $d^{2}$ out of $4 d^{12}$ .

$d^{2} \frac{w^{4}}{d^{2} (4 d^{10})}$

Cancel the common factor.

$d^{2} \frac{w^{4}}{d^{2} (4 d^{10})}$

Rewrite the expression.

$\frac{w^{4}}{4 d^{10}}$

Simplify ((-w^0d)^2)/((-2w^-2d^6)^2)

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