Evaluate
\frac{x^{11}}{y^{2}}
Expand
\frac{x^{11}}{y^{2}}
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\frac{\left(x^{3}\right)^{6}\left(y^{4}\right)^{6}\left(xy^{6}\right)^{-4}}{x^{3}y^{2}}
Expand \left(x^{3}y^{4}\right)^{6}.
\frac{x^{18}\left(y^{4}\right)^{6}\left(xy^{6}\right)^{-4}}{x^{3}y^{2}}
To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.
\frac{x^{18}y^{24}\left(xy^{6}\right)^{-4}}{x^{3}y^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.
\frac{x^{18}y^{24}x^{-4}\left(y^{6}\right)^{-4}}{x^{3}y^{2}}
Expand \left(xy^{6}\right)^{-4}.
\frac{x^{18}y^{24}x^{-4}y^{-24}}{x^{3}y^{2}}
To raise a power to another power, multiply the exponents. Multiply 6 and -4 to get -24.
\frac{x^{14}y^{24}y^{-24}}{x^{3}y^{2}}
To multiply powers of the same base, add their exponents. Add 18 and -4 to get 14.
\frac{x^{14}}{x^{3}y^{2}}
Multiply y^{24} and y^{-24} to get 1.
\frac{x^{11}}{y^{2}}
Cancel out x^{3} in both numerator and denominator.
\frac{\left(x^{3}\right)^{6}\left(y^{4}\right)^{6}\left(xy^{6}\right)^{-4}}{x^{3}y^{2}}
Expand \left(x^{3}y^{4}\right)^{6}.
\frac{x^{18}\left(y^{4}\right)^{6}\left(xy^{6}\right)^{-4}}{x^{3}y^{2}}
To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.
\frac{x^{18}y^{24}\left(xy^{6}\right)^{-4}}{x^{3}y^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.
\frac{x^{18}y^{24}x^{-4}\left(y^{6}\right)^{-4}}{x^{3}y^{2}}
Expand \left(xy^{6}\right)^{-4}.
\frac{x^{18}y^{24}x^{-4}y^{-24}}{x^{3}y^{2}}
To raise a power to another power, multiply the exponents. Multiply 6 and -4 to get -24.
\frac{x^{14}y^{24}y^{-24}}{x^{3}y^{2}}
To multiply powers of the same base, add their exponents. Add 18 and -4 to get 14.
\frac{x^{14}}{x^{3}y^{2}}
Multiply y^{24} and y^{-24} to get 1.
\frac{x^{11}}{y^{2}}
Cancel out x^{3} in both numerator and denominator.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}