Algebra Examples

${(\frac{75}{3})}^{\frac{2}{3}}$

Step 1

Reduce the expression $\frac{75}{3}$ by cancelling the common factors.

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Step 1.1

Factor $3$ out of $75$ .

${(\frac{3 \cdot 25}{3})}^{\frac{2}{3}}$

Step 1.2

Factor $3$ out of $3$ .

${(\frac{3 \cdot 25}{3 (1)})}^{\frac{2}{3}}$

Step 1.3

Cancel the common factor.

${(\frac{3 \cdot 25}{3 \cdot 1})}^{\frac{2}{3}}$

Step 1.4

Rewrite the expression.

${(\frac{25}{1})}^{\frac{2}{3}}$

Step 2

Divide $25$ by $1$ .

$25^{\frac{2}{3}}$

Step 3

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[3]{25^{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{25^{2}}$

Decimal Form:

$8.54987973 \dots$