Algebra Examples

${(\frac{1}{3} x^{5})}^{3} \cdot 81 x^{4}$

Step 1

Rewrite using the commutative property of multiplication.

$81 {(\frac{1}{3} x^{5})}^{3} x^{4}$

Step 2

Combine $\frac{1}{3}$ and $x^{5}$ .

$81 {(\frac{x^{5}}{3})}^{3} x^{4}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{x^{5}}{3}$ .

$81 \frac{{(x^{5})}^{3}}{3^{3}} x^{4}$

Step 3.2

Multiply the exponents in ${(x^{5})}^{3}$ .

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Step 3.2.1

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

$81 \frac{x^{5 \cdot 3}}{3^{3}} x^{4}$

Step 3.2.2

Multiply $5$ by $3$ .

$81 \frac{x^{15}}{3^{3}} x^{4}$

Step 3.3

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

$81 \frac{x^{15}}{27} x^{4}$

Step 4

Cancel the common factor of $27$ .

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Step 4.1

Factor $27$ out of $81$ .

$27 (3) \frac{x^{15}}{27} x^{4}$

Step 4.2

Cancel the common factor.

$27 \cdot 3 \frac{x^{15}}{27} x^{4}$

Step 4.3

Rewrite the expression.

$3 x^{15} x^{4}$

Step 5

Multiply $x^{15}$ by $x^{4}$ by adding the exponents.

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Step 5.1

Move $x^{4}$ .

$3 (x^{4} x^{15})$

Step 5.2

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

$3 x^{4 + 15}$

Step 5.3

Add $4$ and $15$ .

$3 x^{19}$