Simplify 3/( square root of x)+x/( cube root of y)

$\frac{3}{\sqrt{x}} + \frac{x}{\sqrt[3]{y}}$

Step 1

Simplify each term.

Multiply $\frac{3}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{3}{\sqrt{x}} \cdot \frac{\sqrt{x}}{\sqrt{x}} + \frac{x}{\sqrt[3]{y}}$

Combine and simplify the denominator.

Multiply $\frac{3}{\sqrt{x}}$ by $\frac{\sqrt{x}}{\sqrt{x}}$ .

$\frac{3 \sqrt{x}}{\sqrt{x} \sqrt{x}} + \frac{x}{\sqrt[3]{y}}$

Raise $\sqrt{x}$ to the power of $1$ .

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

Raise $\sqrt{x}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

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

$\frac{3 \sqrt{x}}{{(x^{\frac{1}{2}})}^{2}} + \frac{x}{\sqrt[3]{y}}$

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$\frac{3 \sqrt{x}}{x} + \frac{x}{\sqrt[3]{y}}$

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

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

Combine and simplify the denominator.

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

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

Raise $\sqrt[3]{y}$ to the power of $1$ .

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

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

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

Add $1$ and $2$ .

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

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

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

$\frac{3 \sqrt{x}}{x} + \frac{x {\sqrt[3]{y}}^{2}}{{(y^{\frac{1}{3}})}^{3}}$

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Rewrite ${\sqrt[3]{y}}^{2}$ as ${(y^{2})}^{\frac{1}{3}}$ .

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

Step 2

To write $\frac{3 \sqrt{x}}{x}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

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

Step 3

To write $\frac{x \sqrt[3]{y^{2}}}{y}$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

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

Step 4

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

Multiply $\frac{3 \sqrt{x}}{x}$ by $\frac{y}{y}$ .

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

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

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

Reorder the factors of $y x$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

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

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

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{y^{2}}$ as $y^{\frac{2}{3}}$ .

$\frac{3 x^{\frac{1}{2}} y + x y^{\frac{2}{3}} x}{x y}$

Factor $x^{\frac{1}{2}} y^{\frac{2}{3}}$ out of $3 x^{\frac{1}{2}} y + x y^{\frac{2}{3}} x$ .

Move $y^{\frac{2}{3}}$ .

$\frac{3 x^{\frac{1}{2}} y + x \cdot x y^{\frac{2}{3}}}{x y}$

Factor $x^{\frac{1}{2}} y^{\frac{2}{3}}$ out of $3 x^{\frac{1}{2}} y$ .

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}}) + x \cdot x y^{\frac{2}{3}}}{x y}$

Factor $x^{\frac{1}{2}} y^{\frac{2}{3}}$ out of $x \cdot x y^{\frac{2}{3}}$ .

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}}) + x^{\frac{1}{2}} y^{\frac{2}{3}} (x^{\frac{1}{2}} x)}{x y}$

Factor $x^{\frac{1}{2}} y^{\frac{2}{3}}$ out of $x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}}) + x^{\frac{1}{2}} y^{\frac{2}{3}} (x^{\frac{1}{2}} x)$ .

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{1}{2}} x)}{x y}$

Multiply $x^{\frac{1}{2}}$ by $x$ by adding the exponents.

Multiply $x^{\frac{1}{2}}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{1}{2}} x^{1})}{x y}$

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

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{1}{2} + 1})}{x y}$

Write $1$ as a fraction with a common denominator.

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{1}{2} + \frac{2}{2}})}{x y}$

Combine the numerators over the common denominator.

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{1 + 2}{2}})}{x y}$

Add $1$ and $2$ .

$\frac{x^{\frac{1}{2}} y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{3}{2}})}{x y}$

Step 7

Simplify.

Move $x^{\frac{1}{2}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{y^{\frac{2}{3}} (3 y^{\frac{1}{3}} + x^{\frac{3}{2}})}{x y x^{- \frac{1}{2}}}$

Move $y^{\frac{2}{3}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x y x^{- \frac{1}{2}} y^{- \frac{2}{3}}}$

Step 8

Simplify the denominator.

Multiply $x$ by $x^{- \frac{1}{2}}$ by adding the exponents.

Move $x^{- \frac{1}{2}}$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{- \frac{1}{2}} x y \cdot y^{- \frac{2}{3}}}$

Multiply $x^{- \frac{1}{2}}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{- \frac{1}{2}} x^{1} y \cdot y^{- \frac{2}{3}}}$

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

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{- \frac{1}{2} + 1} y \cdot y^{- \frac{2}{3}}}$

Write $1$ as a fraction with a common denominator.

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{- \frac{1}{2} + \frac{2}{2}} y \cdot y^{- \frac{2}{3}}}$

Combine the numerators over the common denominator.

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{- 1 + 2}{2}} y \cdot y^{- \frac{2}{3}}}$

Add $- 1$ and $2$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} y \cdot y^{- \frac{2}{3}}}$

Multiply $y$ by $y^{- \frac{2}{3}}$ by adding the exponents.

Move $y^{- \frac{2}{3}}$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} (y^{- \frac{2}{3}} y)}$

Multiply $y^{- \frac{2}{3}}$ by $y$ .

Raise $y$ to the power of $1$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} (y^{- \frac{2}{3}} y^{1})}$

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

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} y^{- \frac{2}{3} + 1}}$

Write $1$ as a fraction with a common denominator.

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} y^{- \frac{2}{3} + \frac{3}{3}}}$

Combine the numerators over the common denominator.

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} y^{\frac{- 2 + 3}{3}}}$

Add $- 2$ and $3$ .

$\frac{3 y^{\frac{1}{3}} + x^{\frac{3}{2}}}{x^{\frac{1}{2}} y^{\frac{1}{3}}}$

Simplify 3/( square root of x)+x/( cube root of y)

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