Basic Math Examples

$\frac{{(w^{2} z^{4})}^{3}}{{(- w z^{5})}^{2} (w^{4} z^{2})}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $w^{2} z^{4}$ .

$\frac{{(w^{2})}^{3} {(z^{4})}^{3}}{{(- w z^{5})}^{2} w^{4} z^{2}}$

Step 1.2

Multiply the exponents in ${(w^{2})}^{3}$ .

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Step 1.2.1

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

$\frac{w^{2 \cdot 3} {(z^{4})}^{3}}{{(- w z^{5})}^{2} w^{4} z^{2}}$

Step 1.2.2

Multiply $2$ by $3$ .

$\frac{w^{6} {(z^{4})}^{3}}{{(- w z^{5})}^{2} w^{4} z^{2}}$

Step 1.3

Multiply the exponents in ${(z^{4})}^{3}$ .

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Step 1.3.1

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

$\frac{w^{6} z^{4 \cdot 3}}{{(- w z^{5})}^{2} w^{4} z^{2}}$

Step 1.3.2

Multiply $4$ by $3$ .

$\frac{w^{6} z^{12}}{{(- w z^{5})}^{2} w^{4} z^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $- w z^{5}$ .

$\frac{w^{6} z^{12}}{{(- w)}^{2} {(z^{5})}^{2} w^{4} z^{2}}$

Step 2.2

Combine exponents.

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Step 2.2.1

Factor $- 1$ out of $- w$ .

$\frac{w^{6} z^{12}}{{(- (w))}^{2} {(z^{5})}^{2} w^{4} z^{2}}$

Step 2.2.2

Rewrite $- (w)$ as $- 1 (w)$ .

$\frac{w^{6} z^{12}}{{(- 1 (w))}^{2} {(z^{5})}^{2} w^{4} z^{2}}$

Step 2.2.3

Apply the product rule to $- 1 (w)$ .

$\frac{w^{6} z^{12}}{{(- 1)}^{2} w^{2} {(z^{5})}^{2} w^{4} z^{2}}$

Step 2.2.4

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

$\frac{w^{6} z^{12}}{1 w^{2} {(z^{5})}^{2} w^{4} z^{2}}$

Step 2.2.5

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

$\frac{w^{6} z^{12}}{w^{2} {(z^{5})}^{2} w^{4} z^{2}}$

Step 2.2.6

Multiply $w^{2}$ by $w^{4}$ by adding the exponents.

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Step 2.2.6.1

Move $w^{4}$ .

$\frac{w^{6} z^{12}}{w^{4} w^{2} {(z^{5})}^{2} z^{2}}$

Step 2.2.6.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{w^{6} z^{12}}{w^{4 + 2} {(z^{5})}^{2} z^{2}}$

Step 2.2.6.3

Add $4$ and $2$ .

$\frac{w^{6} z^{12}}{w^{6} {(z^{5})}^{2} z^{2}}$

Step 2.3

Multiply the exponents in ${(z^{5})}^{2}$ .

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Step 2.3.1

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

$\frac{w^{6} z^{12}}{w^{6} z^{5 \cdot 2} z^{2}}$

Step 2.3.2

Multiply $5$ by $2$ .

$\frac{w^{6} z^{12}}{w^{6} z^{10} z^{2}}$

Step 2.4

Multiply $z^{10}$ by $z^{2}$ by adding the exponents.

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Step 2.4.1

Move $z^{2}$ .

$\frac{w^{6} z^{12}}{w^{6} (z^{2} z^{10})}$

Step 2.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{w^{6} z^{12}}{w^{6} z^{2 + 10}}$

Step 2.4.3

Add $2$ and $10$ .

$\frac{w^{6} z^{12}}{w^{6} z^{12}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $w^{6}$ .

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Step 3.1.1

Cancel the common factor.

$\frac{w^{6} z^{12}}{w^{6} z^{12}}$

Step 3.1.2

Rewrite the expression.

$\frac{z^{12}}{z^{12}}$

Step 3.2

Cancel the common factor of $z^{12}$ .

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Step 3.2.1

Cancel the common factor.

$\frac{z^{12}}{z^{12}}$

Step 3.2.2

Rewrite the expression.

$1$