Algebra Examples

${(\frac{3^{6}}{3^{4}})}^{2} \cdot x^{- 3} \cdot x^{4}$

Step 1

Multiply $x^{- 3}$ by $x^{4}$ by adding the exponents.

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Step 1.1

Move $x^{4}$ .

${(\frac{3^{6}}{3^{4}})}^{2} \cdot (x^{4} x^{- 3})$

Step 1.2

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

${(\frac{3^{6}}{3^{4}})}^{2} \cdot x^{4 - 3}$

Step 1.3

Subtract $3$ from $4$ .

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

Step 2

Simplify ${(\frac{3^{6}}{3^{4}})}^{2} \cdot x^{1}$ .

${(\frac{3^{6}}{3^{4}})}^{2} \cdot x$

Step 3

Cancel the common factor of $3^{6}$ and $3^{4}$ .

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Step 3.1

Factor $3^{4}$ out of $3^{6}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

Divide $3^{2}$ by $1$ .

${(3^{2})}^{2} \cdot x$

Step 4

Simplify the expression.

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Step 4.1

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

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Step 4.1.1

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

$3^{2 \cdot 2} \cdot x$

Step 4.1.2

Multiply $2$ by $2$ .

$3^{4} \cdot x$

Step 4.2

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

$81 x$