Evaluate
\frac{y^{2}}{x^{12}}
Expand
\frac{y^{2}}{x^{12}}
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\frac{\left(x^{2}\right)^{2}}{\left(y^{3}\right)^{2}}\times \left(\frac{y^{4}}{x^{8}}\right)^{2}
To raise \frac{x^{2}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x^{2}\right)^{2}}{\left(y^{3}\right)^{2}}\times \frac{\left(y^{4}\right)^{2}}{\left(x^{8}\right)^{2}}
To raise \frac{y^{4}}{x^{8}} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x^{2}\right)^{2}\left(y^{4}\right)^{2}}{\left(y^{3}\right)^{2}\left(x^{8}\right)^{2}}
Multiply \frac{\left(x^{2}\right)^{2}}{\left(y^{3}\right)^{2}} times \frac{\left(y^{4}\right)^{2}}{\left(x^{8}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{x^{4}\left(y^{4}\right)^{2}}{\left(y^{3}\right)^{2}\left(x^{8}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\frac{x^{4}y^{8}}{\left(y^{3}\right)^{2}\left(x^{8}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.
\frac{x^{4}y^{8}}{y^{6}\left(x^{8}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\frac{x^{4}y^{8}}{y^{6}x^{16}}
To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.
\frac{y^{2}}{x^{12}}
Cancel out x^{4}y^{6} in both numerator and denominator.
\frac{\left(x^{2}\right)^{2}}{\left(y^{3}\right)^{2}}\times \left(\frac{y^{4}}{x^{8}}\right)^{2}
To raise \frac{x^{2}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x^{2}\right)^{2}}{\left(y^{3}\right)^{2}}\times \frac{\left(y^{4}\right)^{2}}{\left(x^{8}\right)^{2}}
To raise \frac{y^{4}}{x^{8}} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(x^{2}\right)^{2}\left(y^{4}\right)^{2}}{\left(y^{3}\right)^{2}\left(x^{8}\right)^{2}}
Multiply \frac{\left(x^{2}\right)^{2}}{\left(y^{3}\right)^{2}} times \frac{\left(y^{4}\right)^{2}}{\left(x^{8}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.
\frac{x^{4}\left(y^{4}\right)^{2}}{\left(y^{3}\right)^{2}\left(x^{8}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\frac{x^{4}y^{8}}{\left(y^{3}\right)^{2}\left(x^{8}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.
\frac{x^{4}y^{8}}{y^{6}\left(x^{8}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\frac{x^{4}y^{8}}{y^{6}x^{16}}
To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.
\frac{y^{2}}{x^{12}}
Cancel out x^{4}y^{6} 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}