Basic Math Examples

$\frac{(51 z^{5} y^{- 3} a) (19 z y^{- 7})}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 1

Multiply $z^{5}$ by $z$ by adding the exponents.

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Step 1.1

Move $z$ .

$\frac{51 (z \cdot z^{5}) y^{- 3} a (19 y^{- 7})}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 1.2

Multiply $z$ by $z^{5}$ .

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Step 1.2.1

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

$\frac{51 (z^{1} z^{5}) y^{- 3} a (19 y^{- 7})}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 1.2.2

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

$\frac{51 z^{1 + 5} y^{- 3} a (19 y^{- 7})}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 1.3

Add $1$ and $5$ .

$\frac{51 z^{6} y^{- 3} a (19 y^{- 7})}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 2

Multiply $y^{- 3}$ by $y^{- 7}$ by adding the exponents.

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Step 2.1

Move $y^{- 7}$ .

$\frac{51 z^{6} (y^{- 7} y^{- 3}) a \cdot 19}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 2.2

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

$\frac{51 z^{6} y^{- 7 - 3} a \cdot 19}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 2.3

Subtract $3$ from $- 7$ .

$\frac{51 z^{6} y^{- 10} a \cdot 19}{(59 z^{4} y^{2} a^{- 1}) (17 z^{- 5} y)}$

Step 3

Multiply $z^{4}$ by $z^{- 5}$ by adding the exponents.

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Step 3.1

Move $z^{- 5}$ .

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 (z^{- 5} z^{4}) y^{2} a^{- 1} (17 y)}$

Step 3.2

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

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 z^{- 5 + 4} y^{2} a^{- 1} (17 y)}$

Step 3.3

Add $- 5$ and $4$ .

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 z^{- 1} y^{2} a^{- 1} (17 y)}$

Step 4

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 4.1

Move $y$ .

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 z^{- 1} (y \cdot y^{2}) a^{- 1} \cdot 17}$

Step 4.2

Multiply $y$ by $y^{2}$ .

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Step 4.2.1

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

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 z^{- 1} (y^{1} y^{2}) a^{- 1} \cdot 17}$

Step 4.2.2

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

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 z^{- 1} y^{1 + 2} a^{- 1} \cdot 17}$

Step 4.3

Add $1$ and $2$ .

$\frac{51 z^{6} y^{- 10} a \cdot 19}{59 z^{- 1} y^{3} a^{- 1} \cdot 17}$

Step 5

Move $y^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{51 z^{6} a \cdot 19}{59 z^{- 1} y^{3} a^{- 1} \cdot 17 y^{10}}$

Step 6

Multiply $y^{3}$ by $y^{10}$ by adding the exponents.

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Step 6.1

Move $y^{10}$ .

$\frac{51 z^{6} a \cdot 19}{59 z^{- 1} (y^{10} y^{3}) a^{- 1} \cdot 17}$

Step 6.2

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

$\frac{51 z^{6} a \cdot 19}{59 z^{- 1} y^{10 + 3} a^{- 1} \cdot 17}$

Step 6.3

Add $10$ and $3$ .

$\frac{51 z^{6} a \cdot 19}{59 z^{- 1} y^{13} a^{- 1} \cdot 17}$

Step 7

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

$\frac{51 z^{6} a \cdot 19 z}{59 y^{13} a^{- 1} \cdot 17}$

Step 8

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

$\frac{51 z^{6} a \cdot 19 z a}{59 y^{13} \cdot 17}$

Step 9

Simplify the numerator.

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Step 9.1

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

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Step 9.1.1

Move $z$ .

$\frac{51 (z \cdot z^{6}) a \cdot 19 a}{59 y^{13} \cdot 17}$

Step 9.1.2

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

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Step 9.1.2.1

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

$\frac{51 (z^{1} z^{6}) a \cdot 19 a}{59 y^{13} \cdot 17}$

Step 9.1.2.2

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

$\frac{51 z^{1 + 6} a \cdot 19 a}{59 y^{13} \cdot 17}$

Step 9.1.3

Add $1$ and $6$ .

$\frac{51 z^{7} a \cdot 19 a}{59 y^{13} \cdot 17}$

Step 9.2

Multiply $a$ by $a$ by adding the exponents.

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Step 9.2.1

Move $a$ .

$\frac{51 z^{7} (a \cdot a) \cdot 19}{59 y^{13} \cdot 17}$

Step 9.2.2

Multiply $a$ by $a$ .

$\frac{51 z^{7} a^{2} \cdot 19}{59 y^{13} \cdot 17}$

Step 10

Cancel the common factor of $51$ and $17$ .

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Step 10.1

Factor $17$ out of $51 z^{7} a^{2} \cdot 19$ .

$\frac{17 (3 z^{7} a^{2} \cdot 19)}{59 y^{13} \cdot 17}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $17$ out of $59 y^{13} \cdot 17$ .

$\frac{17 (3 z^{7} a^{2} \cdot 19)}{17 \cdot (59 y^{13})}$

Step 10.2.2

Cancel the common factor.

$\frac{17 (3 z^{7} a^{2} \cdot 19)}{17 \cdot (59 y^{13})}$

Step 10.2.3

Rewrite the expression.

$\frac{3 z^{7} a^{2} \cdot 19}{59 y^{13}}$

Step 11

Multiply $19$ by $3$ .

$\frac{57 z^{7} a^{2}}{59 y^{13}}$