Algebra Examples

$- 7 + {(16 p + 8)}^{\frac{1}{3}} = - 1$

Step 1

Move all terms not containing $p$ to the right side of the equation.

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Step 1.1

Add $7$ to both sides of the equation.

${(16 p + 8)}^{\frac{1}{3}} = - 1 + 7$

Step 1.2

Add $- 1$ and $7$ .

${(16 p + 8)}^{\frac{1}{3}} = 6$

Step 2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${({(16 p + 8)}^{\frac{1}{3}})}^{3} = 6^{3}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify ${({(16 p + 8)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1

Multiply the exponents in ${({(16 p + 8)}^{\frac{1}{3}})}^{3}$ .

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Step 3.1.1.1.1

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

${(16 p + 8)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Step 3.1.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

${(16 p + 8)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Step 3.1.1.1.2.2

Rewrite the expression.

${(16 p + 8)}^{1} = 6^{3}$

Step 3.1.1.2

Simplify.

$16 p + 8 = 6^{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

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

$16 p + 8 = 216$

Step 4

Solve for $p$ .

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Step 4.1

Move all terms not containing $p$ to the right side of the equation.

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Step 4.1.1

Subtract $8$ from both sides of the equation.

$16 p = 216 - 8$

Step 4.1.2

Subtract $8$ from $216$ .

$16 p = 208$

Step 4.2

Divide each term in $16 p = 208$ by $16$ and simplify.

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Step 4.2.1

Divide each term in $16 p = 208$ by $16$ .

$\frac{16 p}{16} = \frac{208}{16}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $16$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{16 p}{16} = \frac{208}{16}$

Step 4.2.2.1.2

Divide $p$ by $1$ .

$p = \frac{208}{16}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $208$ by $16$ .

$p = 13$