Evaluate
\frac{1}{y^{27}x^{81}}
Expand
\frac{1}{y^{27}x^{81}}
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\left(x^{9}y^{3}\right)^{-9}
Use the rules of exponents to simplify the expression.
\left(x^{9}\right)^{-9}\left(y^{3}\right)^{-9}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
x^{9\left(-9\right)}y^{3\left(-9\right)}
To raise a power to another power, multiply the exponents.
\frac{1}{x^{81}}y^{3\left(-9\right)}
Multiply 9 times -9.
\frac{1}{x^{81}}\times \frac{1}{y^{27}}
Multiply 3 times -9.
\left(x^{9}y^{3}\right)^{-9}
Use the rules of exponents to simplify the expression.
\left(x^{9}\right)^{-9}\left(y^{3}\right)^{-9}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
x^{9\left(-9\right)}y^{3\left(-9\right)}
To raise a power to another power, multiply the exponents.
\frac{1}{x^{81}}y^{3\left(-9\right)}
Multiply 9 times -9.
\frac{1}{x^{81}}\times \frac{1}{y^{27}}
Multiply 3 times -9.
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}