Basic Math Examples

${(\frac{- 7 n^{3} m^{9}}{9 n^{9} m})}^{2}$

Step 1

Cancel the common factor of $n^{3}$ and $n^{9}$ .

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Step 1.1

Factor $n^{3}$ out of $- 7 n^{3} m^{9}$ .

${(\frac{n^{3} (- 7 m^{9})}{9 n^{9} m})}^{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $n^{3}$ out of $9 n^{9} m$ .

${(\frac{n^{3} (- 7 m^{9})}{n^{3} (9 n^{6} m)})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{n^{3} (- 7 m^{9})}{n^{3} (9 n^{6} m)})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{- 7 m^{9}}{9 n^{6} m})}^{2}$

Step 2

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

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Step 2.1

Factor $m$ out of $- 7 m^{9}$ .

${(\frac{m (- 7 m^{8})}{9 n^{6} m})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $m$ out of $9 n^{6} m$ .

${(\frac{m (- 7 m^{8})}{m (9 n^{6})})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{m (- 7 m^{8})}{m (9 n^{6})})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{- 7 m^{8}}{9 n^{6}})}^{2}$

Step 3

Move the negative in front of the fraction.

${(- \frac{7 m^{8}}{9 n^{6}})}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $- \frac{7 m^{8}}{9 n^{6}}$ .

${(- 1)}^{2} {(\frac{7 m^{8}}{9 n^{6}})}^{2}$

Step 4.2

Apply the product rule to $\frac{7 m^{8}}{9 n^{6}}$ .

${(- 1)}^{2} \frac{{(7 m^{8})}^{2}}{{(9 n^{6})}^{2}}$

Step 4.3

Apply the product rule to $7 m^{8}$ .

${(- 1)}^{2} \frac{7^{2} {(m^{8})}^{2}}{{(9 n^{6})}^{2}}$

Step 4.4

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

${(- 1)}^{2} \frac{7^{2} {(m^{8})}^{2}}{9^{2} {(n^{6})}^{2}}$

Step 5

Simplify the expression.

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Step 5.1

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

$1 \frac{7^{2} {(m^{8})}^{2}}{9^{2} {(n^{6})}^{2}}$

Step 5.2

Multiply $\frac{7^{2} {(m^{8})}^{2}}{9^{2} {(n^{6})}^{2}}$ by $1$ .

$\frac{7^{2} {(m^{8})}^{2}}{9^{2} {(n^{6})}^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

Raise $7$ to the power of $2$ .

$\frac{49 {(m^{8})}^{2}}{9^{2} {(n^{6})}^{2}}$

Step 6.2

Multiply the exponents in ${(m^{8})}^{2}$ .

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Step 6.2.1

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

$\frac{49 m^{8 \cdot 2}}{9^{2} {(n^{6})}^{2}}$

Step 6.2.2

Multiply $8$ by $2$ .

$\frac{49 m^{16}}{9^{2} {(n^{6})}^{2}}$

Step 7

Simplify the denominator.

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Step 7.1

Raise $9$ to the power of $2$ .

$\frac{49 m^{16}}{81 {(n^{6})}^{2}}$

Step 7.2

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

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Step 7.2.1

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

$\frac{49 m^{16}}{81 n^{6 \cdot 2}}$

Step 7.2.2

Multiply $6$ by $2$ .

$\frac{49 m^{16}}{81 n^{12}}$