Evaluate
\frac{y^{6}}{8x^{9}}
Expand
\frac{y^{6}}{8x^{9}}
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\frac{\left(2x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}
To raise \frac{2x^{3}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(2x^{3}\right)^{-3}}{y^{-6}}
To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.
\frac{2^{-3}\left(x^{3}\right)^{-3}}{y^{-6}}
Expand \left(2x^{3}\right)^{-3}.
\frac{2^{-3}x^{-9}}{y^{-6}}
To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.
\frac{\frac{1}{8}x^{-9}}{y^{-6}}
Calculate 2 to the power of -3 and get \frac{1}{8}.
\frac{\left(2x^{3}\right)^{-3}}{\left(y^{2}\right)^{-3}}
To raise \frac{2x^{3}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(2x^{3}\right)^{-3}}{y^{-6}}
To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.
\frac{2^{-3}\left(x^{3}\right)^{-3}}{y^{-6}}
Expand \left(2x^{3}\right)^{-3}.
\frac{2^{-3}x^{-9}}{y^{-6}}
To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.
\frac{\frac{1}{8}x^{-9}}{y^{-6}}
Calculate 2 to the power of -3 and get \frac{1}{8}.
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}