Basic Math Examples

${({(- 3 n^{- 4} y^{- 2})}^{- 3})}^{- 2}$

Step 1

Multiply the exponents in ${({(- 3 n^{- 4} y^{- 2})}^{- 3})}^{- 2}$ .

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Step 1.1

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

${(- 3 n^{- 4} y^{- 2})}^{- 3 \cdot - 2}$

Step 1.2

Multiply $- 3$ by $- 2$ .

${(- 3 n^{- 4} y^{- 2})}^{6}$

Step 2

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

${(- 3 \frac{1}{n^{4}} y^{- 2})}^{6}$

Step 3

Combine $- 3$ and $\frac{1}{n^{4}}$ .

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

Step 4

Move the negative in front of the fraction.

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

Step 5

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

${(- \frac{3}{n^{4}} \cdot \frac{1}{y^{2}})}^{6}$

Step 6

Multiply $\frac{1}{y^{2}}$ by $\frac{3}{n^{4}}$ .

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

Step 7

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

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Step 7.1

Apply the product rule to $- \frac{3}{y^{2} n^{4}}$ .

${(- 1)}^{6} {(\frac{3}{y^{2} n^{4}})}^{6}$

Step 7.2

Apply the product rule to $\frac{3}{y^{2} n^{4}}$ .

${(- 1)}^{6} \frac{3^{6}}{{(y^{2} n^{4})}^{6}}$

Step 7.3

Apply the product rule to $y^{2} n^{4}$ .

${(- 1)}^{6} \frac{3^{6}}{{(y^{2})}^{6} {(n^{4})}^{6}}$

Step 8

Simplify the expression.

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Step 8.1

Raise $- 1$ to the power of $6$ .

$1 \frac{3^{6}}{{(y^{2})}^{6} {(n^{4})}^{6}}$

Step 8.2

Multiply $\frac{3^{6}}{{(y^{2})}^{6} {(n^{4})}^{6}}$ by $1$ .

$\frac{3^{6}}{{(y^{2})}^{6} {(n^{4})}^{6}}$

Step 8.3

Raise $3$ to the power of $6$ .

$\frac{729}{{(y^{2})}^{6} {(n^{4})}^{6}}$

Step 9

Simplify the denominator.

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Step 9.1

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

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Step 9.1.1

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

$\frac{729}{y^{2 \cdot 6} {(n^{4})}^{6}}$

Step 9.1.2

Multiply $2$ by $6$ .

$\frac{729}{y^{12} {(n^{4})}^{6}}$

Step 9.2

Multiply the exponents in ${(n^{4})}^{6}$ .

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Step 9.2.1

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

$\frac{729}{y^{12} n^{4 \cdot 6}}$

Step 9.2.2

Multiply $4$ by $6$ .

$\frac{729}{y^{12} n^{24}}$