Solve for b b=( cube root of -25)^3

$b = {(\sqrt[3]{- 25})}^{3}$

Remove parentheses.

$b = {\sqrt[3]{- 25}}^{3}$

Simplify ${\sqrt[3]{- 25}}^{3}$ .

Rewrite $- 25$ as ${(- 1)}^{3} \cdot 25$ .

Rewrite $- 25$ as $- 1 (25)$ .

$b = {\sqrt[3]{- 1 (25)}}^{3}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$b = {\sqrt[3]{{(- 1)}^{3} \cdot 25}}^{3}$

Pull terms out from under the radical.

$b = {(- 1 \sqrt[3]{25})}^{3}$

Simplify the expression.

Rewrite $- 1 \sqrt[3]{25}$ as $- \sqrt[3]{25}$ .

$b = {(- \sqrt[3]{25})}^{3}$

Apply the product rule to $- \sqrt[3]{25}$ .

$b = {(- 1)}^{3} {\sqrt[3]{25}}^{3}$

Raise $- 1$ to the power of $3$ .

$b = - {\sqrt[3]{25}}^{3}$

Rewrite ${\sqrt[3]{25}}^{3}$ as $25$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{25}$ as $25^{\frac{1}{3}}$ .

$b = - {(25^{\frac{1}{3}})}^{3}$

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

$b = - 25^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$b = - 25^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$b = - 25^{\frac{3}{3}}$

Rewrite the expression.

$b = - 25^{1}$

Evaluate the exponent.

$b = - 1 \cdot 25$

Multiply $- 1$ by $25$ .

$b = - 25$