Basic Math Examples

$\frac{x^{0} y^{0} z^{- 2}}{(x^{11} y^{- 1} z^{45}) (x^{- 1} y^{0} z^{2})}$

Step 1

Multiply $x^{11}$ by $x^{- 1}$ by adding the exponents.

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Step 1.1

Move $x^{- 1}$ .

$\frac{x^{0} y^{0} z^{- 2}}{x^{- 1} x^{11} y^{- 1} z^{45} (y^{0} z^{2})}$

Step 1.2

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

$\frac{x^{0} y^{0} z^{- 2}}{x^{- 1 + 11} y^{- 1} z^{45} (y^{0} z^{2})}$

Step 1.3

Add $- 1$ and $11$ .

$\frac{x^{0} y^{0} z^{- 2}}{x^{10} y^{- 1} z^{45} (y^{0} z^{2})}$

Step 2

Simplify $x^{10} y^{- 1} z^{45} (y^{0} z^{2})$ .

$\frac{x^{0} y^{0} z^{- 2}}{x^{10} y^{- 1} z^{45} z^{2}}$

Step 3

Multiply $z^{45}$ by $z^{2}$ by adding the exponents.

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Step 3.1

Move $z^{2}$ .

$\frac{x^{0} y^{0} z^{- 2}}{x^{10} y^{- 1} (z^{2} z^{45})}$

Step 3.2

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

$\frac{x^{0} y^{0} z^{- 2}}{x^{10} y^{- 1} z^{2 + 45}}$

Step 3.3

Add $2$ and $45$ .

$\frac{x^{0} y^{0} z^{- 2}}{x^{10} y^{- 1} z^{47}}$

Step 4

Move $x^{0}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{z^{- 2}}{x^{10} y^{- 1} z^{47} x^{0}}$

Step 5

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

$\frac{1}{x^{10} y^{- 1} z^{47} x^{0} z^{2}}$

Step 6

Simplify the denominator.

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Step 6.1

Multiply $x^{10}$ by $x^{0}$ by adding the exponents.

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Step 6.1.1

Move $x^{0}$ .

$\frac{1}{x^{0} x^{10} y^{- 1} z^{47} z^{2}}$

Step 6.1.2

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

$\frac{1}{x^{0 + 10} y^{- 1} z^{47} z^{2}}$

Step 6.1.3

Add $0$ and $10$ .

$\frac{1}{x^{10} y^{- 1} z^{47} z^{2}}$

Step 6.2

Multiply $z^{47}$ by $z^{2}$ by adding the exponents.

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Step 6.2.1

Move $z^{2}$ .

$\frac{1}{x^{10} y^{- 1} (z^{2} z^{47})}$

Step 6.2.2

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

$\frac{1}{x^{10} y^{- 1} z^{2 + 47}}$

Step 6.2.3

Add $2$ and $47$ .

$\frac{1}{x^{10} y^{- 1} z^{49}}$

Step 7

Move $y^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{y}{x^{10} z^{49}}$