Pre-Algebra Examples

${(\frac{3 x^{10} y^{12} z^{7}}{- 6 x^{4} y^{3} z^{4}})}^{2}$

Step 1

Cancel the common factor of $3$ and $- 6$ .

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Step 1.1

Factor $3$ out of $3 x^{10} y^{12} z^{7}$ .

${(\frac{3 (x^{10} y^{12} z^{7})}{- 6 x^{4} y^{3} z^{4}})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

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

${(\frac{3 (x^{10} y^{12} z^{7})}{3 (- 2 x^{4} y^{3} z^{4})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{3 (x^{10} y^{12} z^{7})}{3 (- 2 x^{4} y^{3} z^{4})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{x^{10} y^{12} z^{7}}{- 2 x^{4} y^{3} z^{4}})}^{2}$

Step 2

Cancel the common factor of $x^{10}$ and $x^{4}$ .

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Step 2.1

Factor $x^{4}$ out of $x^{10} y^{12} z^{7}$ .

${(\frac{x^{4} (x^{6} y^{12} z^{7})}{- 2 x^{4} y^{3} z^{4}})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{4}$ out of $- 2 x^{4} y^{3} z^{4}$ .

${(\frac{x^{4} (x^{6} y^{12} z^{7})}{x^{4} (- 2 y^{3} z^{4})})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{x^{4} (x^{6} y^{12} z^{7})}{x^{4} (- 2 y^{3} z^{4})})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{x^{6} y^{12} z^{7}}{- 2 y^{3} z^{4}})}^{2}$

Step 3

Cancel the common factor of $y^{12}$ and $y^{3}$ .

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Step 3.1

Factor $y^{3}$ out of $x^{6} y^{12} z^{7}$ .

${(\frac{y^{3} (x^{6} y^{9} z^{7})}{- 2 y^{3} z^{4}})}^{2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{3}$ out of $- 2 y^{3} z^{4}$ .

${(\frac{y^{3} (x^{6} y^{9} z^{7})}{y^{3} (- 2 z^{4})})}^{2}$

Step 3.2.2

Cancel the common factor.

${(\frac{y^{3} (x^{6} y^{9} z^{7})}{y^{3} (- 2 z^{4})})}^{2}$

Step 3.2.3

Rewrite the expression.

${(\frac{x^{6} y^{9} z^{7}}{- 2 z^{4}})}^{2}$

Step 4

Cancel the common factor of $z^{7}$ and $z^{4}$ .

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Step 4.1

Factor $z^{4}$ out of $x^{6} y^{9} z^{7}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $z^{4}$ out of $- 2 z^{4}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Move the negative in front of the fraction.

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

Step 6

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 6.1

Apply the product rule to $- \frac{x^{6} y^{9} z^{3}}{2}$ .

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

Step 6.2

Apply the product rule to $\frac{x^{6} y^{9} z^{3}}{2}$ .

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

Step 6.3

Apply the product rule to $x^{6} y^{9} z^{3}$ .

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

Step 6.4

Apply the product rule to $x^{6} y^{9}$ .

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

Step 7

Simplify the expression.

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Step 7.1

Raise $- 1$ to the power of $2$ .

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

Step 7.2

Multiply $\frac{{(x^{6})}^{2} {(y^{9})}^{2} {(z^{3})}^{2}}{2^{2}}$ by $1$ .

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

Step 8

Simplify the numerator.

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Step 8.1

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

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Step 8.1.1

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

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

Step 8.1.2

Multiply $6$ by $2$ .

$\frac{x^{12} {(y^{9})}^{2} {(z^{3})}^{2}}{2^{2}}$

Step 8.2

Multiply the exponents in ${(y^{9})}^{2}$ .

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Step 8.2.1

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

$\frac{x^{12} y^{9 \cdot 2} {(z^{3})}^{2}}{2^{2}}$

Step 8.2.2

Multiply $9$ by $2$ .

$\frac{x^{12} y^{18} {(z^{3})}^{2}}{2^{2}}$

Step 8.3

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

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Step 8.3.1

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

$\frac{x^{12} y^{18} z^{3 \cdot 2}}{2^{2}}$

Step 8.3.2

Multiply $3$ by $2$ .

$\frac{x^{12} y^{18} z^{6}}{2^{2}}$

Step 9

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

$\frac{x^{12} y^{18} z^{6}}{4}$