Pre-Algebra Examples

$(2 x^{- 3} y z^{- 6}) {(2 x)}^{- 5}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$2 \frac{1}{x^{3}} y z^{- 6} {(2 x)}^{- 5}$

Step 2

Combine $2$ and $\frac{1}{x^{3}}$ .

$\frac{2}{x^{3}} y z^{- 6} {(2 x)}^{- 5}$

Step 3

Combine $\frac{2}{x^{3}}$ and $y$ .

$\frac{2 y}{x^{3}} z^{- 6} {(2 x)}^{- 5}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 y}{x^{3}} \cdot \frac{1}{z^{6}} {(2 x)}^{- 5}$

Step 5

Combine.

$\frac{2 y \cdot 1}{x^{3} z^{6}} {(2 x)}^{- 5}$

Step 6

Multiply $2$ by $1$ .

$\frac{2 y}{x^{3} z^{6}} {(2 x)}^{- 5}$

Step 7

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 y}{x^{3} z^{6}} \cdot \frac{1}{{(2 x)}^{5}}$

Step 8

Combine fractions.

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Step 8.1

Combine.

$\frac{2 y \cdot 1}{x^{3} z^{6} {(2 x)}^{5}}$

Step 8.2

Multiply $2$ by $1$ .

$\frac{2 y}{x^{3} z^{6} {(2 x)}^{5}}$

Step 9

Simplify the denominator.

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Step 9.1

Apply the product rule to $2 x$ .

$\frac{2 y}{x^{3} z^{6} \cdot 2^{5} x^{5}}$

Step 9.2

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

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Step 9.2.1

Move $x^{5}$ .

$\frac{2 y}{x^{5} x^{3} z^{6} \cdot 2^{5}}$

Step 9.2.2

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

$\frac{2 y}{x^{5 + 3} z^{6} \cdot 2^{5}}$

Step 9.2.3

Add $5$ and $3$ .

$\frac{2 y}{x^{8} z^{6} \cdot 2^{5}}$

Step 9.3

Raise $2$ to the power of $5$ .

$\frac{2 y}{x^{8} z^{6} \cdot 32}$

Step 10

Reduce the expression by cancelling the common factors.

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Step 10.1

Cancel the common factor of $2$ and $32$ .

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Step 10.1.1

Factor $2$ out of $2 y$ .

$\frac{2 (y)}{x^{8} z^{6} \cdot 32}$

Step 10.1.2

Cancel the common factors.

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Step 10.1.2.1

Factor $2$ out of $x^{8} z^{6} \cdot 32$ .

$\frac{2 (y)}{2 (x^{8} z^{6} \cdot 16)}$

Step 10.1.2.2

Cancel the common factor.

$\frac{2 y}{2 (x^{8} z^{6} \cdot 16)}$

Step 10.1.2.3

Rewrite the expression.

$\frac{y}{x^{8} z^{6} \cdot 16}$

Step 10.2

Move $16$ to the left of $x^{8} z^{6}$ .

$\frac{y}{16 x^{8} z^{6}}$