Evaluate
\frac{y^{6}}{x^{9}}
Expand
\frac{y^{6}}{x^{9}}
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\left(\frac{x^{3}}{y^{2}}\right)^{-3}
Use the rules of exponents to simplify the expression.
\frac{\left(x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}
To raise the quotient of two numbers to a power, raise each number to the power and then divide.
\frac{x^{3\left(-3\right)}}{y^{2\left(-3\right)}}
To raise a power to another power, multiply the exponents.
\frac{x^{-9}}{y^{2\left(-3\right)}}
Multiply 3 times -3.
\frac{1}{x^{9}y^{-6}}
Multiply 2 times -3.
\left(\frac{x^{3}}{y^{2}}\right)^{-3}
Use the rules of exponents to simplify the expression.
\frac{\left(x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}
To raise the quotient of two numbers to a power, raise each number to the power and then divide.
\frac{x^{3\left(-3\right)}}{y^{2\left(-3\right)}}
To raise a power to another power, multiply the exponents.
\frac{x^{-9}}{y^{2\left(-3\right)}}
Multiply 3 times -3.
\frac{1}{x^{9}y^{-6}}
Multiply 2 times -3.
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}