Algebra Examples

$x^{\frac{3}{4}} + 10 = 0$

Step 1

Subtract $10$ from both sides of the equation.

$x^{\frac{3}{4}} = - 10$

Step 2

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

${(x^{\frac{3}{4}})}^{\frac{4}{3}} = {(- 10)}^{\frac{4}{3}}$

Step 3

Simplify the left side.

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Step 3.1

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

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Step 3.1.1

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

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Step 3.1.1.1

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

$x^{\frac{3}{4} \cdot \frac{4}{3}} = {(- 10)}^{\frac{4}{3}}$

Step 3.1.1.2

Cancel the common factor of $3$ .

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Step 3.1.1.2.1

Cancel the common factor.

$x^{\frac{3}{4} \cdot \frac{4}{3}} = {(- 10)}^{\frac{4}{3}}$

Step 3.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{4} \cdot 4} = {(- 10)}^{\frac{4}{3}}$

Step 3.1.1.3

Cancel the common factor of $4$ .

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Step 3.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{4} \cdot 4} = {(- 10)}^{\frac{4}{3}}$

Step 3.1.1.3.2

Rewrite the expression.

$x^{1} = {(- 10)}^{\frac{4}{3}}$

Step 3.1.2

Simplify.

$x = {(- 10)}^{\frac{4}{3}}$

Step 4

Exclude the solutions that do not make $x^{\frac{3}{4}} + 10 = 0$ true.

$No solution$