Algebra Examples

$3^{2} \cdot {(3^{3})}^{2} \cdot 3^{- 8}$

Step 1

Multiply $3^{2}$ by $3^{- 8}$ by adding the exponents.

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Step 1.1

Move $3^{- 8}$ .

$3^{- 8} \cdot 3^{2} \cdot {(3^{3})}^{2}$

Step 1.2

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

$3^{- 8 + 2} \cdot {(3^{3})}^{2}$

Step 1.3

Add $- 8$ and $2$ .

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

Step 2

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

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Multiply $3$ by $2$ .

$\frac{1}{729} \cdot 3^{6}$

Step 3.3

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

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

Step 4

Cancel the common factor of $729$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$1$