Evaluate
\frac{\left(\frac{y}{z}\right)^{12}}{x^{10}}
Expand
\frac{\left(\frac{y}{z}\right)^{12}}{x^{10}}
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\left(\frac{x^{-2}\times \frac{1}{z}y^{6}}{x^{3}z^{5}}\right)^{2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(\frac{y^{6}}{x^{5}z^{6}}\right)^{2}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{\left(y^{6}\right)^{2}}{\left(x^{5}z^{6}\right)^{2}}
To raise \frac{y^{6}}{x^{5}z^{6}} to a power, raise both numerator and denominator to the power and then divide.
\frac{y^{12}}{\left(x^{5}z^{6}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.
\frac{y^{12}}{\left(x^{5}\right)^{2}\left(z^{6}\right)^{2}}
Expand \left(x^{5}z^{6}\right)^{2}.
\frac{y^{12}}{x^{10}\left(z^{6}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
\frac{y^{12}}{x^{10}z^{12}}
To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.
\left(\frac{x^{-2}\times \frac{1}{z}y^{6}}{x^{3}z^{5}}\right)^{2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(\frac{y^{6}}{x^{5}z^{6}}\right)^{2}
To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.
\frac{\left(y^{6}\right)^{2}}{\left(x^{5}z^{6}\right)^{2}}
To raise \frac{y^{6}}{x^{5}z^{6}} to a power, raise both numerator and denominator to the power and then divide.
\frac{y^{12}}{\left(x^{5}z^{6}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.
\frac{y^{12}}{\left(x^{5}\right)^{2}\left(z^{6}\right)^{2}}
Expand \left(x^{5}z^{6}\right)^{2}.
\frac{y^{12}}{x^{10}\left(z^{6}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
\frac{y^{12}}{x^{10}z^{12}}
To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.
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}