Algebra Examples

$p = \sqrt[5]{\frac{q - 4 m}{7 r}}$

Step 1

Rewrite the equation as $\sqrt[5]{\frac{q - 4 m}{7 r}} = p$ .

$\sqrt[5]{\frac{q - 4 m}{7 r}} = p$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{\frac{q - 4 m}{7 r}}}^{5} = p^{5}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{\frac{q - 4 m}{7 r}}$ as ${(\frac{q - 4 m}{7 r})}^{\frac{1}{5}}$ .

${({(\frac{q - 4 m}{7 r})}^{\frac{1}{5}})}^{5} = p^{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(\frac{q - 4 m}{7 r})}^{\frac{1}{5}})}^{5}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(\frac{q - 4 m}{7 r})}^{\frac{1}{5}})}^{5}$ .

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Step 3.2.1.1.1

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

${(\frac{q - 4 m}{7 r})}^{\frac{1}{5} \cdot 5} = p^{5}$

Step 3.2.1.1.2

Cancel the common factor of $5$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(\frac{q - 4 m}{7 r})}^{\frac{1}{5} \cdot 5} = p^{5}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(\frac{q - 4 m}{7 r})}^{1} = p^{5}$

Step 3.2.1.2

Simplify.

$\frac{q - 4 m}{7 r} = p^{5}$

Step 4

Solve for $q$ .

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Step 4.1

Multiply both sides by $7 r$ .

$\frac{q - 4 m}{7 r} (7 r) = p^{5} (7 r)$

Step 4.2

Simplify.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Simplify $\frac{q - 4 m}{7 r} (7 r)$ .

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Step 4.2.1.1.1

Rewrite using the commutative property of multiplication.

$7 \frac{q - 4 m}{7 r} r = p^{5} (7 r)$

Step 4.2.1.1.2

Cancel the common factor of $7$ .

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Step 4.2.1.1.2.1

Factor $7$ out of $7 r$ .

$7 \frac{q - 4 m}{7 (r)} r = p^{5} (7 r)$

Step 4.2.1.1.2.2

Cancel the common factor.

$7 \frac{q - 4 m}{7 r} r = p^{5} (7 r)$

Step 4.2.1.1.2.3

Rewrite the expression.

$\frac{q - 4 m}{r} r = p^{5} (7 r)$

Step 4.2.1.1.3

Cancel the common factor of $r$ .

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Step 4.2.1.1.3.1

Cancel the common factor.

$\frac{q - 4 m}{r} r = p^{5} (7 r)$

Step 4.2.1.1.3.2

Rewrite the expression.

$q - 4 m = p^{5} (7 r)$

Step 4.2.1.1.4

Reorder $q$ and $- 4 m$ .

$- 4 m + q = p^{5} (7 r)$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Rewrite using the commutative property of multiplication.

$- 4 m + q = 7 p^{5} r$

Step 4.3

Add $4 m$ to both sides of the equation.

$q = 7 p^{5} r + 4 m$