Basic Math Examples

{(\frac{6 z^{6} a^{5}}{5 z^{9} a})}^{2}

${(\frac{6 z^{6} a^{5}}{5 z^{9} a})}^{2}$

Step 1

Cancel the common factor of

z^{6}

$z^{6}$ and

z^{9}

$z^{9}$ .

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Step 1.1

Factor

z^{6}

$z^{6}$ out of

6 z^{6} a^{5}

$6 z^{6} a^{5}$ .

{(\frac{z^{6} (6 a^{5})}{5 z^{9} a})}^{2}

${(\frac{z^{6} (6 a^{5})}{5 z^{9} a})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

z^{6}

$z^{6}$ out of

5 z^{9} a

$5 z^{9} a$ .

{(\frac{z^{6} (6 a^{5})}{z^{6} (5 z^{3} a)})}^{2}

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

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

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

Step 2

Cancel the common factor of

$a^{5}$ and

$a$ .

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Step 2.1

Factor

$a$ out of

$6 a^{5}$ .

${(\frac{a (6 a^{4})}{5 z^{3} a})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

$a$ out of

$5 z^{3} a$ .

${(\frac{a (6 a^{4})}{a (5 z^{3})})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{a (6 a^{4})}{a (5 z^{3})})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{6 a^{4}}{5 z^{3}})}^{2}$

${(\frac{6 a^{4}}{5 z^{3}})}^{2}$

${(\frac{6 a^{4}}{5 z^{3}})}^{2}$

Step 3

Use the power rule

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

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Step 3.1

Apply the product rule to

$\frac{6 a^{4}}{5 z^{3}}$ .

$\frac{{(6 a^{4})}^{2}}{{(5 z^{3})}^{2}}$

Step 3.2

Apply the product rule to

$6 a^{4}$ .

$\frac{6^{2} {(a^{4})}^{2}}{{(5 z^{3})}^{2}}$

Step 3.3

Apply the product rule to

$5 z^{3}$ .

$\frac{6^{2} {(a^{4})}^{2}}{5^{2} {(z^{3})}^{2}}$

$\frac{6^{2} {(a^{4})}^{2}}{5^{2} {(z^{3})}^{2}}$

Step 4

Simplify the numerator.

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Step 4.1

Raise

$6$ to the power of

$2$ .

$\frac{36 {(a^{4})}^{2}}{5^{2} {(z^{3})}^{2}}$

Step 4.2

Multiply the exponents in

${(a^{4})}^{2}$ .

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Step 4.2.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{36 a^{4 \cdot 2}}{5^{2} {(z^{3})}^{2}}$

Step 4.2.2

Multiply

$4$ by

$2$ .

$\frac{36 a^{8}}{5^{2} {(z^{3})}^{2}}$

$\frac{36 a^{8}}{5^{2} {(z^{3})}^{2}}$

$\frac{36 a^{8}}{5^{2} {(z^{3})}^{2}}$

Step 5

Simplify the denominator.

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Step 5.1

Raise

$5$ to the power of

$2$ .

$\frac{36 a^{8}}{25 {(z^{3})}^{2}}$

Step 5.2

Multiply the exponents in

${(z^{3})}^{2}$ .

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Step 5.2.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{36 a^{8}}{25 z^{3 \cdot 2}}$

Step 5.2.2

Multiply

$3$ by

$2$ .

$\frac{36 a^{8}}{25 z^{6}}$

$\frac{36 a^{8}}{25 z^{6}}$

$\frac{36 a^{8}}{25 z^{6}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$