Algebra Examples

$\frac{2 {(n^{2})}^{- 5}}{6 v n^{- 3}}$

Step 1

Simplify.

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Step 1.1

Move ${(n^{2})}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2}{6 v n^{- 3} {(n^{2})}^{5}}$

Step 1.2

Move $n^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{2 n^{3}}{6 v {(n^{2})}^{5}}$

Step 2

Cancel the common factor of $2$ and $6$ .

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Step 2.1

Factor $2$ out of $2 n^{3}$ .

$\frac{2 (n^{3})}{6 v {(n^{2})}^{5}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $6 v {(n^{2})}^{5}$ .

$\frac{2 (n^{3})}{2 (3 v {(n^{2})}^{5})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 n^{3}}{2 (3 v {(n^{2})}^{5})}$

Step 2.2.3

Rewrite the expression.

$\frac{n^{3}}{3 v {(n^{2})}^{5}}$

Step 3

Multiply the exponents in ${(n^{2})}^{5}$ .

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Step 3.1

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

$\frac{n^{3}}{3 v n^{2 \cdot 5}}$

Step 3.2

Multiply $2$ by $5$ .

$\frac{n^{3}}{3 v n^{10}}$

Step 4

Cancel the common factor of $n^{3}$ and $n^{10}$ .

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Step 4.1

Multiply by $1$ .

$\frac{n^{3} \cdot 1}{3 v n^{10}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $n^{3}$ out of $3 v n^{10}$ .

$\frac{n^{3} \cdot 1}{n^{3} (3 v n^{7})}$

Step 4.2.2

Cancel the common factor.

$\frac{n^{3} \cdot 1}{n^{3} (3 v n^{7})}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{3 v n^{7}}$