Solve for x -3=-5+ fifth root of 10-x

$- 3 = - 5 + \sqrt[5]{10 - x}$

Step 1

Rewrite the equation as $- 5 + \sqrt[5]{10 - x} = - 3$ .

$- 5 + \sqrt[5]{10 - x} = - 3$

Step 2

Move all terms not containing $\sqrt[5]{10 - x}$ to the right side of the equation.

Add $5$ to both sides of the equation.

$\sqrt[5]{10 - x} = - 3 + 5$

Add $- 3$ and $5$ .

$\sqrt[5]{10 - x} = 2$

Step 3

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

${\sqrt[5]{10 - x}}^{5} = 2^{5}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{10 - x}$ as ${(10 - x)}^{\frac{1}{5}}$ .

${({(10 - x)}^{\frac{1}{5}})}^{5} = 2^{5}$

Simplify the left side.

Simplify ${({(10 - x)}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(10 - x)}^{\frac{1}{5}})}^{5}$ .

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

${(10 - x)}^{\frac{1}{5} \cdot 5} = 2^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(10 - x)}^{\frac{1}{5} \cdot 5} = 2^{5}$

Rewrite the expression.

${(10 - x)}^{1} = 2^{5}$

Simplify.

$10 - x = 2^{5}$

Simplify the right side.

Raise $2$ to the power of $5$ .

$10 - x = 32$

Step 5

Solve for $x$ .

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

Subtract $10$ from both sides of the equation.

$- x = 32 - 10$

Subtract $10$ from $32$ .

$- x = 22$

Divide each term in $- x = 22$ by $- 1$ and simplify.

Divide each term in $- x = 22$ by $- 1$ .

$\frac{- x}{- 1} = \frac{22}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{22}{- 1}$

Divide $x$ by $1$ .

$x = \frac{22}{- 1}$

Simplify the right side.

Divide $22$ by $- 1$ .

$x = - 22$

Solve for x -3=-5+ fifth root of 10-x

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