Algebra Examples

$3^{- 6} \cdot {(3^{4} \div 3^{0})}^{2}$

Step 1

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

$\frac{1}{3^{6}} \cdot {(3^{4} \div 3^{0})}^{2}$

Step 2

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

$\frac{1}{729} \cdot {(3^{4} \div 3^{0})}^{2}$

Step 3

Rewrite the division as a fraction.

$\frac{1}{729} \cdot {(\frac{3^{4}}{3^{0}})}^{2}$

Step 4

Cancel the common factor of $3^{4}$ and $3^{0}$ .

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Step 4.1

Factor $3^{0}$ out of $3^{4}$ .

$\frac{1}{729} \cdot {(\frac{3^{0} \cdot 3^{4}}{3^{0}})}^{2}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Multiply by $1$ .

$\frac{1}{729} \cdot {(\frac{3^{0} \cdot 3^{4}}{3^{0} \cdot 1})}^{2}$

Step 4.2.2

Cancel the common factor.

$\frac{1}{729} \cdot {(\frac{3^{0} \cdot 3^{4}}{3^{0} \cdot 1})}^{2}$

Step 4.2.3

Rewrite the expression.

$\frac{1}{729} \cdot {(\frac{3^{4}}{1})}^{2}$

Step 4.2.4

Divide $3^{4}$ by $1$ .

$\frac{1}{729} \cdot {(3^{4})}^{2}$

Step 5

Simplify the expression.

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Step 5.1

Multiply the exponents in ${(3^{4})}^{2}$ .

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Step 5.1.1

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

$\frac{1}{729} \cdot 3^{4 \cdot 2}$

Step 5.1.2

Multiply $4$ by $2$ .

$\frac{1}{729} \cdot 3^{8}$

Step 5.2

Raise $3$ to the power of $8$ .

$\frac{1}{729} \cdot 6561$

Step 6

Cancel the common factor of $729$ .

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Step 6.1

Factor $729$ out of $6561$ .

$\frac{1}{729} \cdot (729 (9))$

Step 6.2

Cancel the common factor.

$\frac{1}{729} \cdot (729 \cdot 9)$

Step 6.3

Rewrite the expression.

$9$