Evaluate
\frac{y^{9}}{x^{8}}
Expand
\frac{y^{9}}{x^{8}}
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\frac{x^{12}y^{-21}}{\left(x^{4}\right)^{5}\left(y^{-6}\right)^{5}}
Expand \left(x^{4}y^{-6}\right)^{5}.
\frac{x^{12}y^{-21}}{x^{20}\left(y^{-6}\right)^{5}}
To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.
\frac{x^{12}y^{-21}}{x^{20}y^{-30}}
To raise a power to another power, multiply the exponents. Multiply -6 and 5 to get -30.
\frac{y^{-21}}{y^{-30}x^{8}}
Cancel out x^{12} in both numerator and denominator.
\frac{y^{9}}{x^{8}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{x^{12}y^{-21}}{\left(x^{4}\right)^{5}\left(y^{-6}\right)^{5}}
Expand \left(x^{4}y^{-6}\right)^{5}.
\frac{x^{12}y^{-21}}{x^{20}\left(y^{-6}\right)^{5}}
To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.
\frac{x^{12}y^{-21}}{x^{20}y^{-30}}
To raise a power to another power, multiply the exponents. Multiply -6 and 5 to get -30.
\frac{y^{-21}}{y^{-30}x^{8}}
Cancel out x^{12} in both numerator and denominator.
\frac{y^{9}}{x^{8}}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
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}