Evaluate
\frac{16\times \left(\frac{ab}{c}\right)^{4}}{81}
Expand
\frac{16\times \left(\frac{ab}{c}\right)^{4}}{81}
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\frac{\left(-2ab\right)^{4}}{\left(3c\right)^{4}}
To raise \frac{-2ab}{3c} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(-2\right)^{4}a^{4}b^{4}}{\left(3c\right)^{4}}
Expand \left(-2ab\right)^{4}.
\frac{16a^{4}b^{4}}{\left(3c\right)^{4}}
Calculate -2 to the power of 4 and get 16.
\frac{16a^{4}b^{4}}{3^{4}c^{4}}
Expand \left(3c\right)^{4}.
\frac{16a^{4}b^{4}}{81c^{4}}
Calculate 3 to the power of 4 and get 81.
\frac{\left(-2ab\right)^{4}}{\left(3c\right)^{4}}
To raise \frac{-2ab}{3c} to a power, raise both numerator and denominator to the power and then divide.
\frac{\left(-2\right)^{4}a^{4}b^{4}}{\left(3c\right)^{4}}
Expand \left(-2ab\right)^{4}.
\frac{16a^{4}b^{4}}{\left(3c\right)^{4}}
Calculate -2 to the power of 4 and get 16.
\frac{16a^{4}b^{4}}{3^{4}c^{4}}
Expand \left(3c\right)^{4}.
\frac{16a^{4}b^{4}}{81c^{4}}
Calculate 3 to the power of 4 and get 81.
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}