Basic Math Examples

${(\frac{a w^{4}}{2})}^{4} \cdot {(\frac{w^{4} a}{2})}^{- 1}$

Step 1

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

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Step 1.1

Apply the product rule to $\frac{a w^{4}}{2}$ .

$\frac{{(a w^{4})}^{4}}{2^{4}} \cdot {(\frac{w^{4} a}{2})}^{- 1}$

Step 1.2

Apply the product rule to $a w^{4}$ .

$\frac{a^{4} {(w^{4})}^{4}}{2^{4}} \cdot {(\frac{w^{4} a}{2})}^{- 1}$

Step 2

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

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Step 2.1

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

$\frac{a^{4} w^{4 \cdot 4}}{2^{4}} \cdot {(\frac{w^{4} a}{2})}^{- 1}$

Step 2.2

Multiply $4$ by $4$ .

$\frac{a^{4} w^{16}}{2^{4}} \cdot {(\frac{w^{4} a}{2})}^{- 1}$

Step 3

Raise $2$ to the power of $4$ .

$\frac{a^{4} w^{16}}{16} \cdot {(\frac{w^{4} a}{2})}^{- 1}$

Step 4

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

$\frac{a^{4} w^{16}}{16} \cdot \frac{2}{w^{4} a}$

Step 5

Combine.

$\frac{a^{4} w^{16} \cdot 2}{16 (w^{4} a)}$

Step 6

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

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Step 6.1

Factor $a$ out of $a^{4} w^{16} \cdot 2$ .

$\frac{a (a^{3} w^{16} \cdot 2)}{16 (w^{4} a)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $a$ out of $16 (w^{4} a)$ .

$\frac{a (a^{3} w^{16} \cdot 2)}{a (16 (w^{4}))}$

Step 6.2.2

Cancel the common factor.

$\frac{a (a^{3} w^{16} \cdot 2)}{a (16 (w^{4}))}$

Step 6.2.3

Rewrite the expression.

$\frac{a^{3} w^{16} \cdot 2}{16 (w^{4})}$

Step 7

Cancel the common factor of $w^{16}$ and $w^{4}$ .

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Step 7.1

Factor $w^{4}$ out of $a^{3} w^{16} \cdot 2$ .

$\frac{w^{4} (a^{3} w^{12} \cdot 2)}{16 (w^{4})}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $w^{4}$ out of $16 (w^{4})$ .

$\frac{w^{4} (a^{3} w^{12} \cdot 2)}{w^{4} \cdot 16}$

Step 7.2.2

Cancel the common factor.

$\frac{w^{4} (a^{3} w^{12} \cdot 2)}{w^{4} \cdot 16}$

Step 7.2.3

Rewrite the expression.

$\frac{a^{3} w^{12} \cdot 2}{16}$

Step 8

Cancel the common factor of $2$ and $16$ .

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Step 8.1

Factor $2$ out of $a^{3} w^{12} \cdot 2$ .

$\frac{2 \cdot (a^{3} w^{12})}{16}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $16$ .

$\frac{2 \cdot (a^{3} w^{12})}{2 \cdot 8}$

Step 8.2.2

Cancel the common factor.

$\frac{2 \cdot (a^{3} w^{12})}{2 \cdot 8}$

Step 8.2.3

Rewrite the expression.

$\frac{a^{3} w^{12}}{8}$