Pre-Algebra Examples

$(\frac{x^{2} y^{- 3} z^{- 2}}{x^{4} y z^{- 3}}) (\frac{2 x b \cdot (3 y^{2})}{4 a x y^{- 3}})$

Step 1

Combine.

$\frac{x^{2} y^{- 3} z^{- 2} (2 x b \cdot (3 y^{2}))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 2

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

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Step 2.1

Move $x$ .

$\frac{x \cdot x^{2} y^{- 3} z^{- 2} (2 b \cdot (3 y^{2}))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 2.2

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

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Step 2.2.1

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

$\frac{x^{1} x^{2} y^{- 3} z^{- 2} (2 b \cdot (3 y^{2}))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 2.2.2

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

$\frac{x^{1 + 2} y^{- 3} z^{- 2} (2 b \cdot (3 y^{2}))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 2.3

Add $1$ and $2$ .

$\frac{x^{3} y^{- 3} z^{- 2} (2 b \cdot (3 y^{2}))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 3

Multiply $y^{- 3}$ by $y^{2}$ by adding the exponents.

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Step 3.1

Move $y^{2}$ .

$\frac{x^{3} (y^{2} y^{- 3}) z^{- 2} (2 b \cdot (3))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 3.2

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

$\frac{x^{3} y^{2 - 3} z^{- 2} (2 b \cdot (3))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 3.3

Subtract $3$ from $2$ .

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{4} y z^{- 3} (4 a x y^{- 3})}$

Step 4

Multiply $x^{4}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x \cdot x^{4} y z^{- 3} (4 a y^{- 3})}$

Step 4.2

Multiply $x$ by $x^{4}$ .

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Step 4.2.1

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

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{1} x^{4} y z^{- 3} (4 a y^{- 3})}$

Step 4.2.2

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

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{1 + 4} y z^{- 3} (4 a y^{- 3})}$

Step 4.3

Add $1$ and $4$ .

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{5} y z^{- 3} (4 a y^{- 3})}$

Step 5

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

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Step 5.1

Move $y^{- 3}$ .

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{5} (y^{- 3} y) z^{- 3} (4 a)}$

Step 5.2

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

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Step 5.2.1

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

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{5} (y^{- 3} y^{1}) z^{- 3} (4 a)}$

Step 5.2.2

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

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{5} y^{- 3 + 1} z^{- 3} (4 a)}$

Step 5.3

Add $- 3$ and $1$ .

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3))}{x^{5} y^{- 2} z^{- 3} (4 a)}$

Step 6

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

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3)) y^{2}}{x^{5} z^{- 3} (4 a)}$

Step 7

Move $z^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{3} y^{- 1} z^{- 2} (2 b \cdot (3)) y^{2} z^{3}}{x^{5} (4 a)}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $y^{- 1}$ by $y^{2}$ by adding the exponents.

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Step 8.1.1

Move $y^{2}$ .

$\frac{x^{3} (y^{2} y^{- 1}) z^{- 2} (2 b \cdot (3)) z^{3}}{x^{5} (4 a)}$

Step 8.1.2

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

$\frac{x^{3} y^{2 - 1} z^{- 2} (2 b \cdot (3)) z^{3}}{x^{5} (4 a)}$

Step 8.1.3

Subtract $1$ from $2$ .

$\frac{x^{3} y^{1} z^{- 2} (2 b \cdot (3)) z^{3}}{x^{5} (4 a)}$

Step 8.2

Simplify $x^{3} y^{1} z^{- 2} (2 b \cdot (3))$ .

$\frac{x^{3} y z^{- 2} (2 b \cdot (3)) z^{3}}{x^{5} (4 a)}$

Step 8.3

Multiply $z^{- 2}$ by $z^{3}$ by adding the exponents.

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Step 8.3.1

Move $z^{3}$ .

$\frac{x^{3} y (z^{3} z^{- 2}) (2 b \cdot (3))}{x^{5} (4 a)}$

Step 8.3.2

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

$\frac{x^{3} y z^{3 - 2} (2 b \cdot (3))}{x^{5} (4 a)}$

Step 8.3.3

Subtract $2$ from $3$ .

$\frac{x^{3} y z^{1} (2 b \cdot (3))}{x^{5} (4 a)}$

Step 8.4

Simplify $x^{3} y z^{1} (2 b \cdot (3))$ .

$\frac{x^{3} y z (2 b \cdot (3))}{x^{5} (4 a)}$

Step 9

Cancel the common factor of $x^{3}$ and $x^{5}$ .

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Step 9.1

Factor $x^{3}$ out of $x^{3} y z (2 b \cdot (3))$ .

$\frac{x^{3} (y z (2 b \cdot (3)))}{x^{5} (4 a)}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $x^{3}$ out of $x^{5} (4 a)$ .

$\frac{x^{3} (y z (2 b \cdot (3)))}{x^{3} (x^{2} (4 a))}$

Step 9.2.2

Cancel the common factor.

$\frac{x^{3} (y z (2 b \cdot (3)))}{x^{3} (x^{2} (4 a))}$

Step 9.2.3

Rewrite the expression.

$\frac{y z (2 b \cdot (3))}{x^{2} (4 a)}$

Step 10

Cancel the common factor of $2$ and $4$ .

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Step 10.1

Factor $2$ out of $y z (2 b \cdot (3))$ .

$\frac{2 (y z (b \cdot (3)))}{x^{2} (4 a)}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $2$ out of $x^{2} (4 a)$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 11

Reorder.

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Step 11.1

Move $3$ to the left of $y z b$ .

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

Step 11.2

Move $2$ to the left of $x^{2}$ .

$\frac{3 y z b}{2 x^{2} a}$