Evaluate
\frac{4z^{6}}{81y^{2}x^{8}}
Expand
\frac{4z^{6}}{81y^{2}x^{8}}
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\frac{3^{-4}\left(x^{2}\right)^{-4}}{\left(-2y^{-1}z^{3}\right)^{-2}}
Expand \left(3x^{2}\right)^{-4}.
\frac{3^{-4}x^{-8}}{\left(-2y^{-1}z^{3}\right)^{-2}}
To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.
\frac{\frac{1}{81}x^{-8}}{\left(-2y^{-1}z^{3}\right)^{-2}}
Calculate 3 to the power of -4 and get \frac{1}{81}.
\frac{\frac{1}{81}x^{-8}}{\left(-2\right)^{-2}\left(y^{-1}\right)^{-2}\left(z^{3}\right)^{-2}}
Expand \left(-2y^{-1}z^{3}\right)^{-2}.
\frac{\frac{1}{81}x^{-8}}{\left(-2\right)^{-2}y^{2}\left(z^{3}\right)^{-2}}
To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.
\frac{\frac{1}{81}x^{-8}}{\left(-2\right)^{-2}y^{2}z^{-6}}
To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.
\frac{\frac{1}{81}x^{-8}}{\frac{1}{4}y^{2}z^{-6}}
Calculate -2 to the power of -2 and get \frac{1}{4}.
\frac{3^{-4}\left(x^{2}\right)^{-4}}{\left(-2y^{-1}z^{3}\right)^{-2}}
Expand \left(3x^{2}\right)^{-4}.
\frac{3^{-4}x^{-8}}{\left(-2y^{-1}z^{3}\right)^{-2}}
To raise a power to another power, multiply the exponents. Multiply 2 and -4 to get -8.
\frac{\frac{1}{81}x^{-8}}{\left(-2y^{-1}z^{3}\right)^{-2}}
Calculate 3 to the power of -4 and get \frac{1}{81}.
\frac{\frac{1}{81}x^{-8}}{\left(-2\right)^{-2}\left(y^{-1}\right)^{-2}\left(z^{3}\right)^{-2}}
Expand \left(-2y^{-1}z^{3}\right)^{-2}.
\frac{\frac{1}{81}x^{-8}}{\left(-2\right)^{-2}y^{2}\left(z^{3}\right)^{-2}}
To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.
\frac{\frac{1}{81}x^{-8}}{\left(-2\right)^{-2}y^{2}z^{-6}}
To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.
\frac{\frac{1}{81}x^{-8}}{\frac{1}{4}y^{2}z^{-6}}
Calculate -2 to the power of -2 and get \frac{1}{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}