Algebra Examples

$\frac{2 b^{7}}{{(3 v^{- 3} b^{- 2})}^{- 5}}$

Step 1

Move ${(3 v^{- 3} b^{- 2})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$2 b^{7} {(3 v^{- 3} b^{- 2})}^{5}$

Step 2

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

$2 b^{7} {(3 \frac{1}{v^{3}} b^{- 2})}^{5}$

Step 3

Combine $3$ and $\frac{1}{v^{3}}$ .

$2 b^{7} {(\frac{3}{v^{3}} b^{- 2})}^{5}$

Step 4

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

$2 b^{7} {(\frac{3}{v^{3}} \cdot \frac{1}{b^{2}})}^{5}$

Step 5

Combine.

$2 b^{7} {(\frac{3 \cdot 1}{v^{3} b^{2}})}^{5}$

Step 6

Multiply $3$ by $1$ .

$2 b^{7} {(\frac{3}{v^{3} b^{2}})}^{5}$

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 $\frac{3}{v^{3} b^{2}}$ .

$2 b^{7} \frac{3^{5}}{{(v^{3} b^{2})}^{5}}$

Step 7.2

Apply the product rule to $v^{3} b^{2}$ .

$2 b^{7} \frac{3^{5}}{{(v^{3})}^{5} {(b^{2})}^{5}}$

Step 8

Raise $3$ to the power of $5$ .

$2 b^{7} \frac{243}{{(v^{3})}^{5} {(b^{2})}^{5}}$

Step 9

Simplify the denominator.

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Step 9.1

Multiply the exponents in ${(v^{3})}^{5}$ .

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Step 9.1.1

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

$2 b^{7} \frac{243}{v^{3 \cdot 5} {(b^{2})}^{5}}$

Step 9.1.2

Multiply $3$ by $5$ .

$2 b^{7} \frac{243}{v^{15} {(b^{2})}^{5}}$

Step 9.2

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

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Step 9.2.1

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

$2 b^{7} \frac{243}{v^{15} b^{2 \cdot 5}}$

Step 9.2.2

Multiply $2$ by $5$ .

$2 b^{7} \frac{243}{v^{15} b^{10}}$

Step 10

Simplify terms.

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Step 10.1

Cancel the common factor of $b^{7}$ .

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Step 10.1.1

Factor $b^{7}$ out of $2 b^{7}$ .

$b^{7} \cdot 2 \frac{243}{v^{15} b^{10}}$

Step 10.1.2

Factor $b^{7}$ out of $v^{15} b^{10}$ .

$b^{7} \cdot 2 \frac{243}{b^{7} (v^{15} b^{3})}$

Step 10.1.3

Cancel the common factor.

$b^{7} \cdot 2 \frac{243}{b^{7} (v^{15} b^{3})}$

Step 10.1.4

Rewrite the expression.

$2 \frac{243}{v^{15} b^{3}}$

Step 10.2

Combine $2$ and $\frac{243}{v^{15} b^{3}}$ .

$\frac{2 \cdot 243}{v^{15} b^{3}}$

Step 10.3

Multiply $2$ by $243$ .

$\frac{486}{v^{15} b^{3}}$