Algebra Examples

$\frac{3^{6}}{3^{- 4}} \cdot 3^{- 1}$

Step 1

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

$\frac{729}{3^{- 4}} \cdot 3^{- 1}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{729}{\frac{1}{3^{4}}} \cdot 3^{- 1}$

Step 2.2

Raise $3$ to the power of $4$ .

$\frac{729}{\frac{1}{81}} \cdot 3^{- 1}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$729 \cdot 81 \cdot 3^{- 1}$

Step 4

Multiply $729$ by $81$ .

$59049 \cdot 3^{- 1}$

Step 5

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

$59049 \cdot \frac{1}{3}$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Factor $3$ out of $59049$ .

$3 (19683) \cdot \frac{1}{3}$

Step 6.2

Cancel the common factor.

$3 \cdot 19683 \cdot \frac{1}{3}$

Step 6.3

Rewrite the expression.

$19683$