Basic Math Examples

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

Step 1

Cancel the common factor of $z^{6}$ and $z^{9}$ .

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Step 1.1

Factor $z^{6}$ out of $6 z^{6} a^{5}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $z^{6}$ out of $5 z^{9} a$ .

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

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.

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

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.

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

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 $5 z^{3}$ .

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

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 $2$ .

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

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 $2$ .

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