Algebra Examples

$\sqrt[3]{- {(y - 9)}^{9}}$

Step 1

Rewrite $- {(y - 9)}^{9}$ as ${(- {(y - 9)}^{3})}^{3}$ .

$\sqrt[3]{{(- {(y - 9)}^{3})}^{3}}$

Step 2

Pull terms out from under the radical, assuming real numbers.

$- {(y - 9)}^{3}$

Step 3

Use the Binomial Theorem.

$- (y^{3} + 3 y^{2} \cdot - 9 + 3 y {(- 9)}^{2} + {(- 9)}^{3})$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $- 9$ by $3$ .

$- (y^{3} - 27 y^{2} + 3 y {(- 9)}^{2} + {(- 9)}^{3})$

Step 4.1.2

Raise $- 9$ to the power of $2$ .

$- (y^{3} - 27 y^{2} + 3 y \cdot 81 + {(- 9)}^{3})$

Step 4.1.3

Multiply $81$ by $3$ .

$- (y^{3} - 27 y^{2} + 243 y + {(- 9)}^{3})$

Step 4.1.4

Raise $- 9$ to the power of $3$ .

$- (y^{3} - 27 y^{2} + 243 y - 729)$

Step 4.2

Apply the distributive property.

$- y^{3} - (- 27 y^{2}) - (243 y) - - 729$

Step 5

Simplify.

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Step 5.1

Multiply $- 27$ by $- 1$ .

$- y^{3} + 27 y^{2} - (243 y) - - 729$

Step 5.2

Multiply $243$ by $- 1$ .

$- y^{3} + 27 y^{2} - 243 y - - 729$

Step 5.3

Multiply $- 1$ by $- 729$ .

$- y^{3} + 27 y^{2} - 243 y + 729$