Algebra Examples

${((27 p^{5}) (- 8 p^{10}))}^{\frac{1}{3}}$

Step 1

Rewrite using the commutative property of multiplication.

${(27 \cdot - 8 p^{5} p^{10})}^{\frac{1}{3}}$

Step 2

Multiply $p^{5}$ by $p^{10}$ by adding the exponents.

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Step 2.1

Move $p^{10}$ .

${(27 \cdot - 8 (p^{10} p^{5}))}^{\frac{1}{3}}$

Step 2.2

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

${(27 \cdot - 8 p^{10 + 5})}^{\frac{1}{3}}$

Step 2.3

Add $10$ and $5$ .

${(27 \cdot - 8 p^{15})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $27$ by $- 8$ .

${(- 216 p^{15})}^{\frac{1}{3}}$

Step 3.2

Apply the product rule to $- 216 p^{15}$ .

${(- 216)}^{\frac{1}{3}} {(p^{15})}^{\frac{1}{3}}$

Step 3.3

Rewrite $- 216$ as ${(- 6)}^{3}$ .

${({(- 6)}^{3})}^{\frac{1}{3}} {(p^{15})}^{\frac{1}{3}}$

Step 3.4

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

${(- 6)}^{3 (\frac{1}{3})} {(p^{15})}^{\frac{1}{3}}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

${(- 6)}^{3 (\frac{1}{3})} {(p^{15})}^{\frac{1}{3}}$

Step 4.2

Rewrite the expression.

${(- 6)}^{1} {(p^{15})}^{\frac{1}{3}}$

Step 5

Simplify the expression.

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Step 5.1

Evaluate the exponent.

$- 6 {(p^{15})}^{\frac{1}{3}}$

Step 5.2

Multiply the exponents in ${(p^{15})}^{\frac{1}{3}}$ .

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Step 5.2.1

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

$- 6 p^{15 (\frac{1}{3})}$

Step 5.2.2

Cancel the common factor of $3$ .

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Step 5.2.2.1

Factor $3$ out of $15$ .

$- 6 p^{3 (5) \frac{1}{3}}$

Step 5.2.2.2

Cancel the common factor.

$- 6 p^{3 \cdot 5 \frac{1}{3}}$

Step 5.2.2.3

Rewrite the expression.

$- 6 p^{5}$