Evaluate
\frac{9}{x^{2}y^{4}}
Expand
\frac{9}{x^{2}y^{4}}
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3^{-2}x^{-2}\left(y^{3}\right)^{-2}\times \left(9y\right)^{2}
Expand \left(3xy^{3}\right)^{-2}.
3^{-2}x^{-2}y^{-6}\times \left(9y\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.
\frac{1}{9}x^{-2}y^{-6}\times \left(9y\right)^{2}
Calculate 3 to the power of -2 and get \frac{1}{9}.
\frac{1}{9}x^{-2}y^{-6}\times 9^{2}y^{2}
Expand \left(9y\right)^{2}.
\frac{1}{9}x^{-2}y^{-6}\times 81y^{2}
Calculate 9 to the power of 2 and get 81.
9x^{-2}y^{-6}y^{2}
Multiply \frac{1}{9} and 81 to get 9.
9x^{-2}y^{-4}
To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.
3^{-2}x^{-2}\left(y^{3}\right)^{-2}\times \left(9y\right)^{2}
Expand \left(3xy^{3}\right)^{-2}.
3^{-2}x^{-2}y^{-6}\times \left(9y\right)^{2}
To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.
\frac{1}{9}x^{-2}y^{-6}\times \left(9y\right)^{2}
Calculate 3 to the power of -2 and get \frac{1}{9}.
\frac{1}{9}x^{-2}y^{-6}\times 9^{2}y^{2}
Expand \left(9y\right)^{2}.
\frac{1}{9}x^{-2}y^{-6}\times 81y^{2}
Calculate 9 to the power of 2 and get 81.
9x^{-2}y^{-6}y^{2}
Multiply \frac{1}{9} and 81 to get 9.
9x^{-2}y^{-4}
To multiply powers of the same base, add their exponents. Add -6 and 2 to get -4.
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}