Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

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

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

Step 1.2

Move ${(3^{2})}^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(3^{2})}^{6}}{3}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply the exponents in ${(3^{2})}^{6}$ .

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Step 2.1.1

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

$\frac{3^{2 \cdot 6}}{3}$

Step 2.1.2

Multiply $2$ by $6$ .

$\frac{3^{12}}{3}$

Step 2.2

Raise $3$ to the power of $12$ .

$\frac{531441}{3}$

Step 3

Divide $531441$ by $3$ .

$177147$