Simplify ( cube root of 5^2)/( fifth root of 5)

$\frac{\sqrt[3]{5^{2}}}{\sqrt[5]{5}}$

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

$\frac{\sqrt[3]{25}}{\sqrt[5]{5}}$

Multiply $\frac{\sqrt[3]{25}}{\sqrt[5]{5}}$ by $\frac{{\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{4}}$ .

$\frac{\sqrt[3]{25}}{\sqrt[5]{5}} \cdot \frac{{\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{4}}$

Combine and simplify the denominator.

Multiply $\frac{\sqrt[3]{25}}{\sqrt[5]{5}}$ by $\frac{{\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{4}}$ .

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{\sqrt[5]{5} {\sqrt[5]{5}}^{4}}$

Raise $\sqrt[5]{5}$ to the power of $1$ .

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{1} {\sqrt[5]{5}}^{4}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{1 + 4}}$

Add $1$ and $4$ .

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{{\sqrt[5]{5}}^{5}}$

Rewrite ${\sqrt[5]{5}}^{5}$ as $5$ .

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

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{{(5^{\frac{1}{5}})}^{5}}$

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

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{5^{\frac{1}{5} \cdot 5}}$

Combine $\frac{1}{5}$ and $5$ .

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{5^{\frac{5}{5}}}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{5^{\frac{5}{5}}}$

Rewrite the expression.

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{5^{1}}$

Evaluate the exponent.

$\frac{\sqrt[3]{25} {\sqrt[5]{5}}^{4}}{5}$

Simplify the numerator.

Rewrite ${\sqrt[5]{5}}^{4}$ as ${(5^{4})}^{\frac{1}{5}}$ .

$\frac{\sqrt[3]{25} \sqrt[5]{5^{4}}}{5}$

Raise $5$ to the power of $4$ .

$\frac{\sqrt[3]{25} \sqrt[5]{625}}{5}$

Simplify the numerator.

Rewrite the expression using the least common index of $15$ .

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

$\frac{25^{\frac{1}{3}} \sqrt[5]{625}}{5}$

Rewrite $25^{\frac{1}{3}}$ as $25^{\frac{5}{15}}$ .

$\frac{25^{\frac{5}{15}} \sqrt[5]{625}}{5}$

Rewrite $25^{\frac{5}{15}}$ as $\sqrt[15]{25^{5}}$ .

$\frac{\sqrt[15]{25^{5}} \sqrt[5]{625}}{5}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{625}$ as $625^{\frac{1}{5}}$ .

$\frac{\sqrt[15]{25^{5}} \cdot 625^{\frac{1}{5}}}{5}$

Rewrite $625^{\frac{1}{5}}$ as $625^{\frac{3}{15}}$ .

$\frac{\sqrt[15]{25^{5}} \cdot 625^{\frac{3}{15}}}{5}$

Rewrite $625^{\frac{3}{15}}$ as $\sqrt[15]{625^{3}}$ .

$\frac{\sqrt[15]{25^{5}} \sqrt[15]{625^{3}}}{5}$

Combine using the product rule for radicals.

$\frac{\sqrt[15]{25^{5} \cdot 625^{3}}}{5}$

Rewrite $25$ as $5^{2}$ .

$\frac{\sqrt[15]{{(5^{2})}^{5} \cdot 625^{3}}}{5}$

Multiply the exponents in ${(5^{2})}^{5}$ .

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

$\frac{\sqrt[15]{5^{2 \cdot 5} \cdot 625^{3}}}{5}$

Multiply $2$ by $5$ .

$\frac{\sqrt[15]{5^{10} \cdot 625^{3}}}{5}$

Rewrite $625$ as $5^{4}$ .

$\frac{\sqrt[15]{5^{10} \cdot {(5^{4})}^{3}}}{5}$

Multiply the exponents in ${(5^{4})}^{3}$ .

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

$\frac{\sqrt[15]{5^{10} \cdot 5^{4 \cdot 3}}}{5}$

Multiply $4$ by $3$ .

$\frac{\sqrt[15]{5^{10} \cdot 5^{12}}}{5}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[15]{5^{10 + 12}}}{5}$

Add $10$ and $12$ .

$\frac{\sqrt[15]{5^{22}}}{5}$

Raise $5$ to the power of $22$ .

$\frac{\sqrt[15]{2384185791015620}}{5}$

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[15]{2384185791015620}}{5}$

Decimal Form:

$2.11926859 \dots$

Simplify ( cube root of 5^2)/( fifth root of 5)

Related Questions

Support LCMGCF.com by disabling your adblocker.