Algebra Examples

$\frac{{(3 b^{- 3})}^{3}}{2 b^{9}}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{3^{3} {(b^{- 3})}^{3}}{2 b^{9}}$

Step 1.2

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

$\frac{27 {(b^{- 3})}^{3}}{2 b^{9}}$

Step 1.3

Multiply the exponents in ${(b^{- 3})}^{3}$ .

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Step 1.3.1

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

$\frac{27 b^{- 3 \cdot 3}}{2 b^{9}}$

Step 1.3.2

Multiply $- 3$ by $3$ .

$\frac{27 b^{- 9}}{2 b^{9}}$

Step 1.4

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

$\frac{27 \frac{1}{b^{9}}}{2 b^{9}}$

Step 2

Combine $27$ and $\frac{1}{b^{9}}$ .

$\frac{\frac{27}{b^{9}}}{2 b^{9}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{27}{b^{9}} \cdot \frac{1}{2 b^{9}}$

Step 4

Combine.

$\frac{27 \cdot 1}{b^{9} (2 b^{9})}$

Step 5

Multiply $b^{9}$ by $b^{9}$ by adding the exponents.

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Step 5.1

Move $b^{9}$ .

$\frac{27 \cdot 1}{b^{9} b^{9} \cdot 2}$

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{27 \cdot 1}{b^{9 + 9} \cdot 2}$

Step 5.3

Add $9$ and $9$ .

$\frac{27 \cdot 1}{b^{18} \cdot 2}$

Step 6

Multiply $27$ by $1$ .

$\frac{27}{b^{18} \cdot 2}$

Step 7

Move $2$ to the left of $b^{18}$ .

$\frac{27}{2 b^{18}}$