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x^{34}y^{78}
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x^{34}y^{78}
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\left(\frac{\left(x^{2}\right)^{-5}\left(y^{-9}\right)^{-5}}{\left(x^{9}y^{-2}\right)^{-3}}\right)^{2}
Expand \left(x^{2}y^{-9}\right)^{-5}.
\left(\frac{x^{-10}\left(y^{-9}\right)^{-5}}{\left(x^{9}y^{-2}\right)^{-3}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.
\left(\frac{x^{-10}y^{45}}{\left(x^{9}y^{-2}\right)^{-3}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply -9 and -5 to get 45.
\left(\frac{x^{-10}y^{45}}{\left(x^{9}\right)^{-3}\left(y^{-2}\right)^{-3}}\right)^{2}
Expand \left(x^{9}y^{-2}\right)^{-3}.
\left(\frac{x^{-10}y^{45}}{x^{-27}\left(y^{-2}\right)^{-3}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 9 and -3 to get -27.
\left(\frac{x^{-10}y^{45}}{x^{-27}y^{6}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.
\left(\frac{x^{-10}y^{39}}{x^{-27}}\right)^{2}
Cancel out y^{6} in both numerator and denominator.
\left(x^{17}y^{39}\right)^{2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(x^{17}\right)^{2}\left(y^{39}\right)^{2}
Expand \left(x^{17}y^{39}\right)^{2}.
x^{34}\left(y^{39}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 17 and 2 to get 34.
x^{34}y^{78}
To raise a power to another power, multiply the exponents. Multiply 39 and 2 to get 78.
\left(\frac{\left(x^{2}\right)^{-5}\left(y^{-9}\right)^{-5}}{\left(x^{9}y^{-2}\right)^{-3}}\right)^{2}
Expand \left(x^{2}y^{-9}\right)^{-5}.
\left(\frac{x^{-10}\left(y^{-9}\right)^{-5}}{\left(x^{9}y^{-2}\right)^{-3}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 2 and -5 to get -10.
\left(\frac{x^{-10}y^{45}}{\left(x^{9}y^{-2}\right)^{-3}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply -9 and -5 to get 45.
\left(\frac{x^{-10}y^{45}}{\left(x^{9}\right)^{-3}\left(y^{-2}\right)^{-3}}\right)^{2}
Expand \left(x^{9}y^{-2}\right)^{-3}.
\left(\frac{x^{-10}y^{45}}{x^{-27}\left(y^{-2}\right)^{-3}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 9 and -3 to get -27.
\left(\frac{x^{-10}y^{45}}{x^{-27}y^{6}}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.
\left(\frac{x^{-10}y^{39}}{x^{-27}}\right)^{2}
Cancel out y^{6} in both numerator and denominator.
\left(x^{17}y^{39}\right)^{2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(x^{17}\right)^{2}\left(y^{39}\right)^{2}
Expand \left(x^{17}y^{39}\right)^{2}.
x^{34}\left(y^{39}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 17 and 2 to get 34.
x^{34}y^{78}
To raise a power to another power, multiply the exponents. Multiply 39 and 2 to get 78.
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}