Algebra Examples

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

Step 1

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

$81 \cdot x \cdot {(\frac{3}{x^{2}})}^{- 2}$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

$81 x \cdot {(\frac{x^{2}}{3})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{x^{2}}{3}$ .

$81 x \cdot \frac{{(x^{2})}^{2}}{3^{2}}$

Step 3.2

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

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Step 3.2.1

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

$81 x \cdot \frac{x^{2 \cdot 2}}{3^{2}}$

Step 3.2.2

Multiply $2$ by $2$ .

$81 x \cdot \frac{x^{4}}{3^{2}}$

Step 3.3

Raise $3$ to the power of $2$ .

$81 x \cdot \frac{x^{4}}{9}$

Step 4

Cancel the common factor of $9$ .

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Step 4.1

Factor $9$ out of $81 x$ .

$9 (9 x) \cdot \frac{x^{4}}{9}$

Step 4.2

Cancel the common factor.

$9 (9 x) \cdot \frac{x^{4}}{9}$

Step 4.3

Rewrite the expression.

$9 x \cdot x^{4}$

Step 5

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

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Step 5.1

Move $x^{4}$ .

$9 (x^{4} x)$

Step 5.2

Multiply $x^{4}$ by $x$ .

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Step 5.2.1

Raise $x$ to the power of $1$ .

$9 (x^{4} x^{1})$

Step 5.2.2

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

$9 x^{4 + 1}$

Step 5.3

Add $4$ and $1$ .

$9 x^{5}$