Simplify ( square root of x^5)/( fourth root of x^3)

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

Simplify the numerator.

Rewrite $x^{5}$ as ${(x^{2})}^{2} x$ .

Factor out $x^{4}$ .

$\frac{\sqrt{x^{4} x}}{\sqrt[4]{x^{3}}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\frac{\sqrt{{(x^{2})}^{2} x}}{\sqrt[4]{x^{3}}}$

Pull terms out from under the radical.

$\frac{x^{2} \sqrt{x}}{\sqrt[4]{x^{3}}}$

Multiply $\frac{x^{2} \sqrt{x}}{\sqrt[4]{x^{3}}}$ by $\frac{{\sqrt[4]{x^{3}}}^{3}}{{\sqrt[4]{x^{3}}}^{3}}$ .

$\frac{x^{2} \sqrt{x}}{\sqrt[4]{x^{3}}} \cdot \frac{{\sqrt[4]{x^{3}}}^{3}}{{\sqrt[4]{x^{3}}}^{3}}$

Simplify terms.

Combine and simplify the denominator.

Multiply $\frac{x^{2} \sqrt{x}}{\sqrt[4]{x^{3}}}$ by $\frac{{\sqrt[4]{x^{3}}}^{3}}{{\sqrt[4]{x^{3}}}^{3}}$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{\sqrt[4]{x^{3}} {\sqrt[4]{x^{3}}}^{3}}$

Raise $\sqrt[4]{x^{3}}$ to the power of $1$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{{\sqrt[4]{x^{3}}}^{1} {\sqrt[4]{x^{3}}}^{3}}$

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

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{{\sqrt[4]{x^{3}}}^{1 + 3}}$

Add $1$ and $3$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{{\sqrt[4]{x^{3}}}^{4}}$

Rewrite ${\sqrt[4]{x^{3}}}^{4}$ as $x^{3}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x^{3}}$ as $x^{\frac{3}{4}}$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{{(x^{\frac{3}{4}})}^{4}}$

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

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{3}{4} \cdot 4}}$

Combine $\frac{3}{4}$ and $4$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{3 \cdot 4}{4}}}$

Multiply $3$ by $4$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{12}{4}}}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{4 \cdot 3}{4}}}$

Cancel the common factors.

Factor $4$ out of $4$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{4 \cdot 3}{4 (1)}}}$

Cancel the common factor.

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{4 \cdot 3}{4 \cdot 1}}}$

Rewrite the expression.

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{\frac{3}{1}}}$

Divide $3$ by $1$ .

$\frac{x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x^{3}}$

Cancel the common factor of $x^{2}$ and $x^{3}$ .

Factor $x^{2}$ out of $x^{2} \sqrt{x} {\sqrt[4]{x^{3}}}^{3}$ .

$\frac{x^{2} (\sqrt{x} {\sqrt[4]{x^{3}}}^{3})}{x^{3}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{3}$ .

$\frac{x^{2} (\sqrt{x} {\sqrt[4]{x^{3}}}^{3})}{x^{2} x}$

Cancel the common factor.

$\frac{x^{2} (\sqrt{x} {\sqrt[4]{x^{3}}}^{3})}{x^{2} x}$

Rewrite the expression.

$\frac{\sqrt{x} {\sqrt[4]{x^{3}}}^{3}}{x}$

Simplify the numerator.

Rewrite ${\sqrt[4]{x^{3}}}^{3}$ as ${({(x^{3})}^{3})}^{\frac{1}{4}}$ .

$\frac{\sqrt{x} \sqrt[4]{{(x^{3})}^{3}}}{x}$

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

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

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

Multiply $3$ by $3$ .

$\frac{\sqrt{x} \sqrt[4]{x^{9}}}{x}$

Rewrite $x^{9}$ as ${(x^{2})}^{4} x$ .

Factor out $x^{8}$ .

$\frac{\sqrt{x} \sqrt[4]{x^{8} x}}{x}$

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

$\frac{\sqrt{x} \sqrt[4]{{(x^{2})}^{4} x}}{x}$

Pull terms out from under the radical.

$\frac{\sqrt{x} x^{2} \sqrt[4]{x}}{x}$

Combine exponents.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$\frac{x^{\frac{1}{2}} x^{2} \sqrt[4]{x}}{x}$

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

$\frac{x^{\frac{1}{2} + 2} \sqrt[4]{x}}{x}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x^{\frac{1}{2} + 2 \cdot \frac{2}{2}} \sqrt[4]{x}}{x}$

Combine $2$ and $\frac{2}{2}$ .

$\frac{x^{\frac{1}{2} + \frac{2 \cdot 2}{2}} \sqrt[4]{x}}{x}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{1 + 2 \cdot 2}{2}} \sqrt[4]{x}}{x}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{x^{\frac{1 + 4}{2}} \sqrt[4]{x}}{x}$

Add $1$ and $4$ .

$\frac{x^{\frac{5}{2}} \sqrt[4]{x}}{x}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{x}$ as $x^{\frac{1}{4}}$ .

$\frac{x^{\frac{5}{2}} x^{\frac{1}{4}}}{x}$

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

$\frac{x^{\frac{5}{2} + \frac{1}{4}}}{x}$

To write $\frac{5}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x^{\frac{5}{2} \cdot \frac{2}{2} + \frac{1}{4}}}{x}$

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5}{2}$ by $\frac{2}{2}$ .

$\frac{x^{\frac{5 \cdot 2}{2 \cdot 2} + \frac{1}{4}}}{x}$

Multiply $2$ by $2$ .

$\frac{x^{\frac{5 \cdot 2}{4} + \frac{1}{4}}}{x}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{5 \cdot 2 + 1}{4}}}{x}$

Simplify the numerator.

Multiply $5$ by $2$ .

$\frac{x^{\frac{10 + 1}{4}}}{x}$

Add $10$ and $1$ .

$\frac{x^{\frac{11}{4}}}{x}$

Move $x^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$x^{\frac{11}{4}} x^{- 1}$

Multiply $x^{\frac{11}{4}}$ by $x^{- 1}$ by adding the exponents.

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

$x^{\frac{11}{4} - 1}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x^{\frac{11}{4} - 1 \cdot \frac{4}{4}}$

Combine $- 1$ and $\frac{4}{4}$ .

$x^{\frac{11}{4} + \frac{- 1 \cdot 4}{4}}$

Combine the numerators over the common denominator.

$x^{\frac{11 - 1 \cdot 4}{4}}$

Simplify the numerator.

Multiply $- 1$ by $4$ .

$x^{\frac{11 - 4}{4}}$

Subtract $4$ from $11$ .

$x^{\frac{7}{4}}$

Simplify ( square root of x^5)/( fourth root of x^3)

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