Basic Math Examples

$\frac{{(x^{2} y z^{3})}^{- 3}}{x y}$

Step 1

Move ${(x^{2} y z^{3})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x y {(x^{2} y z^{3})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $x^{2} y z^{3}$ .

$\frac{1}{x y {(x^{2} y)}^{3} {(z^{3})}^{3}}$

Step 2.2

Apply the product rule to $x^{2} y$ .

$\frac{1}{x y ({(x^{2})}^{3} y^{3}) {(z^{3})}^{3}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{1}{x y (x^{2 \cdot 3} y^{3}) {(z^{3})}^{3}}$

Step 2.3.2

Multiply $2$ by $3$ .

$\frac{1}{x y (x^{6} y^{3}) {(z^{3})}^{3}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1}{x y (x^{6} y^{3}) z^{3 \cdot 3}}$

Step 2.4.2

Multiply $3$ by $3$ .

$\frac{1}{x y (x^{6} y^{3}) z^{9}}$

$\frac{1}{x y x^{6} y^{3} z^{9}}$

Step 2.5

Combine exponents.

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Step 2.5.1

Multiply $x$ by $x^{6}$ by adding the exponents.

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Step 2.5.1.1

Move $x^{6}$ .

$\frac{1}{x^{6} x y \cdot y^{3} z^{9}}$

Step 2.5.1.2

Multiply $x^{6}$ by $x$ .

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Step 2.5.1.2.1

Raise $x$ to the power of $1$ .

$\frac{1}{x^{6} x^{1} y \cdot y^{3} z^{9}}$

Step 2.5.1.2.2

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

$\frac{1}{x^{6 + 1} y \cdot y^{3} z^{9}}$

Step 2.5.1.3

Add $6$ and $1$ .

$\frac{1}{x^{7} y \cdot y^{3} z^{9}}$

Step 2.5.2

Multiply $y$ by $y^{3}$ by adding the exponents.

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Step 2.5.2.1

Move $y^{3}$ .

$\frac{1}{x^{7} (y^{3} y) z^{9}}$

Step 2.5.2.2

Multiply $y^{3}$ by $y$ .

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Step 2.5.2.2.1

Raise $y$ to the power of $1$ .

$\frac{1}{x^{7} (y^{3} y^{1}) z^{9}}$

Step 2.5.2.2.2

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

$\frac{1}{x^{7} y^{3 + 1} z^{9}}$

Step 2.5.2.3

Add $3$ and $1$ .

$\frac{1}{x^{7} y^{4} z^{9}}$