Precalculus Examples

$m^{\frac{3}{4}} + n^{\frac{3}{4}} = 7$

Step 1

Find a common factor $n^{\frac{3}{4}}$ that is present in each term.

$m^{\frac{3}{4}} + n^{\frac{3}{4}} - 7$

Step 2

Substitute $u$ for $n^{\frac{3}{4}}$ .

$m^{\frac{3}{4}} + u - 7 = 0$

Step 3

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

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Step 3.1

Subtract $m^{\frac{3}{4}}$ from both sides of the equation.

$u - 7 = - m^{\frac{3}{4}}$

Step 3.2

Add $7$ to both sides of the equation.

$u = - m^{\frac{3}{4}} + 7$

Step 4

Substitute $m$ for $u$ .

$n^{\frac{3}{4}} = - m^{\frac{3}{4}} + 7$

Step 5

Subtract $n^{\frac{3}{4}}$ from both sides of the equation.

$m^{\frac{3}{4}} = 7 - n^{\frac{3}{4}}$

Step 6

Raise each side of the equation to the power of $\frac{4}{3}$ to eliminate the fractional exponent on the left side.

${(m^{\frac{3}{4}})}^{\frac{4}{3}} = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$

Step 7

Simplify the left side.

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Step 7.1

Simplify ${(m^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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Step 7.1.1

Multiply the exponents in ${(m^{\frac{3}{4}})}^{\frac{4}{3}}$ .

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Step 7.1.1.1

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

$m^{\frac{3}{4} \cdot \frac{4}{3}} = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$

Step 7.1.1.2

Cancel the common factor of $3$ .

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Step 7.1.1.2.1

Cancel the common factor.

$m^{\frac{3}{4} \cdot \frac{4}{3}} = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$

Step 7.1.1.2.2

Rewrite the expression.

$m^{\frac{1}{4} \cdot 4} = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$

Step 7.1.1.3

Cancel the common factor of $4$ .

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Step 7.1.1.3.1

Cancel the common factor.

$m^{\frac{1}{4} \cdot 4} = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$

Step 7.1.1.3.2

Rewrite the expression.

$m^{1} = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$

Step 7.1.2

Simplify.

$m = {(7 - n^{\frac{3}{4}})}^{\frac{4}{3}}$