Pre-Algebra Examples

${(\frac{9 x^{4} y^{- 6} z^{4}}{3 x y^{- 6} z^{- 2}})}^{- 2}$

Step 1

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

${(\frac{9 x^{4} y^{- 6} z^{4} z^{2}}{3 x y^{- 6}})}^{- 2}$

Step 2

Multiply $z^{4}$ by $z^{2}$ by adding the exponents.

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Step 2.1

Move $z^{2}$ .

${(\frac{9 x^{4} y^{- 6} (z^{2} z^{4})}{3 x y^{- 6}})}^{- 2}$

Step 2.2

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

${(\frac{9 x^{4} y^{- 6} z^{2 + 4}}{3 x y^{- 6}})}^{- 2}$

Step 2.3

Add $2$ and $4$ .

${(\frac{9 x^{4} y^{- 6} z^{6}}{3 x y^{- 6}})}^{- 2}$

Step 3

Cancel the common factor of $9$ and $3$ .

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Step 3.1

Factor $3$ out of $9 x^{4} y^{- 6} z^{6}$ .

${(\frac{3 (3 x^{4} y^{- 6} z^{6})}{3 x y^{- 6}})}^{- 2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 x y^{- 6}$ .

${(\frac{3 (3 x^{4} y^{- 6} z^{6})}{3 (x y^{- 6})})}^{- 2}$

Step 3.2.2

Cancel the common factor.

${(\frac{3 (3 x^{4} y^{- 6} z^{6})}{3 (x y^{- 6})})}^{- 2}$

Step 3.2.3

Rewrite the expression.

${(\frac{3 x^{4} y^{- 6} z^{6}}{x y^{- 6}})}^{- 2}$

Step 4

Cancel the common factor of $x^{4}$ and $x$ .

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Step 4.1

Factor $x$ out of $3 x^{4} y^{- 6} z^{6}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $x y^{- 6}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $y^{- 6}$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $3 x^{3} z^{6}$ by $1$ .

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

Step 6

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

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

Step 7

Simplify the denominator.

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Step 7.1

Apply the product rule to $3 x^{3} z^{6}$ .

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

Step 7.2

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

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

Step 7.3

Raise $3$ to the power of $2$ .

$\frac{1}{9 {(x^{3})}^{2} {(z^{6})}^{2}}$

Step 7.4

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

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Step 7.4.1

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

$\frac{1}{9 x^{3 \cdot 2} {(z^{6})}^{2}}$

Step 7.4.2

Multiply $3$ by $2$ .

$\frac{1}{9 x^{6} {(z^{6})}^{2}}$

Step 7.5

Multiply the exponents in ${(z^{6})}^{2}$ .

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Step 7.5.1

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

$\frac{1}{9 x^{6} z^{6 \cdot 2}}$

Step 7.5.2

Multiply $6$ by $2$ .

$\frac{1}{9 x^{6} z^{12}}$