What is ((x^{2/3}y^{1/3})/(x^{1/2)y^{3/4}})^6 ?

The solution to ((x^{2/3}y^{1/3})/(x^{1/2)y^{3/4}})^6 is x/(y^{5/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ((x^{2/3}y^{1/3})/(x^{1/2)y^{3/4}})^6

simplify

(\frac{x ^{\frac{2}{3}} y ^{\frac{1}{3}}}{x ^{\frac{1}{2}} y ^{\frac{3}{4}}})^{6}

\frac{x}{y ^{\frac{5}{2}}}

Solution steps

(\frac{x ^{\frac{2}{3}} y ^{\frac{1}{3}}}{x ^{\frac{1}{2}} y ^{\frac{3}{4}}})^{6}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( x ^{\frac{2}{3}} y ^{\frac{1}{3}} ) ^{6}}{( x ^{\frac{1}{2}} y ^{\frac{3}{4}} ) ^{6}}

Simplify

(x^{\frac{2}{3}} y^{\frac{1}{3}})^{6} : x^{4} y^{2}

= \frac{x ^{4} y ^{2}}{( x ^{\frac{1}{2}} y ^{\frac{3}{4}} ) ^{6}}

Simplify

(x^{\frac{1}{2}} y^{\frac{3}{4}})^{6} : x^{3} y^{\frac{9}{2}}

= \frac{x ^{4} y ^{2}}{x ^{3} y ^{\frac{9}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{x ^{4}}{x ^{3}} = x^{4 - 3}

= \frac{y ^{2} x ^{4 - 3}}{y ^{\frac{9}{2}}}

Subtract the numbers:

4 - 3 = 1

= \frac{x y ^{2}}{y ^{\frac{9}{2}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{y ^{2}}{y ^{\frac{9}{2}}} = \frac{1}{y ^{\frac{9}{2} - 2}}

= \frac{x}{y ^{\frac{9}{2} - 2}}

Subtract the numbers:

\frac{9}{2} - 2 = \frac{5}{2}

= \frac{x}{y ^{\frac{5}{2}}}

\frac{27}{125} \div 12

\frac{0.54}{0.75} \cdot 100

(1 0^{2})^{2}

2 x^{2} \cdot 3

What is ((x^{2/3}y^{1/3})/(x^{1/2)y^{3/4}})^6 ?
The solution to ((x^{2/3}y^{1/3})/(x^{1/2)y^{3/4}})^6 is x/(y^{5/2)}