Evaluate
\frac{27y}{64x}
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\frac{27y}{64x}
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\left(\frac{x}{y}\right)^{2}\times \left(\frac{3y}{4x}\right)^{3}
Cancel out 2 in both numerator and denominator.
\frac{x^{2}}{y^{2}}\times \left(\frac{3y}{4x}\right)^{3}
To raise \frac{x}{y} to a power, raise both numerator and denominator to the power and then divide.
\frac{x^{2}}{y^{2}}\times \frac{\left(3y\right)^{3}}{\left(4x\right)^{3}}
To raise \frac{3y}{4x} to a power, raise both numerator and denominator to the power and then divide.
\frac{x^{2}\times \left(3y\right)^{3}}{y^{2}\times \left(4x\right)^{3}}
Multiply \frac{x^{2}}{y^{2}} times \frac{\left(3y\right)^{3}}{\left(4x\right)^{3}} by multiplying numerator times numerator and denominator times denominator.
\frac{x^{2}\times 3^{3}y^{3}}{y^{2}\times \left(4x\right)^{3}}
Expand \left(3y\right)^{3}.
\frac{x^{2}\times 27y^{3}}{y^{2}\times \left(4x\right)^{3}}
Calculate 3 to the power of 3 and get 27.
\frac{x^{2}\times 27y^{3}}{y^{2}\times 4^{3}x^{3}}
Expand \left(4x\right)^{3}.
\frac{x^{2}\times 27y^{3}}{y^{2}\times 64x^{3}}
Calculate 4 to the power of 3 and get 64.
\frac{27y}{64x}
Cancel out x^{2}y^{2} in both numerator and denominator.
\left(\frac{x}{y}\right)^{2}\times \left(\frac{3y}{4x}\right)^{3}
Cancel out 2 in both numerator and denominator.
\frac{x^{2}}{y^{2}}\times \left(\frac{3y}{4x}\right)^{3}
To raise \frac{x}{y} to a power, raise both numerator and denominator to the power and then divide.
\frac{x^{2}}{y^{2}}\times \frac{\left(3y\right)^{3}}{\left(4x\right)^{3}}
To raise \frac{3y}{4x} to a power, raise both numerator and denominator to the power and then divide.
\frac{x^{2}\times \left(3y\right)^{3}}{y^{2}\times \left(4x\right)^{3}}
Multiply \frac{x^{2}}{y^{2}} times \frac{\left(3y\right)^{3}}{\left(4x\right)^{3}} by multiplying numerator times numerator and denominator times denominator.
\frac{x^{2}\times 3^{3}y^{3}}{y^{2}\times \left(4x\right)^{3}}
Expand \left(3y\right)^{3}.
\frac{x^{2}\times 27y^{3}}{y^{2}\times \left(4x\right)^{3}}
Calculate 3 to the power of 3 and get 27.
\frac{x^{2}\times 27y^{3}}{y^{2}\times 4^{3}x^{3}}
Expand \left(4x\right)^{3}.
\frac{x^{2}\times 27y^{3}}{y^{2}\times 64x^{3}}
Calculate 4 to the power of 3 and get 64.
\frac{27y}{64x}
Cancel out x^{2}y^{2} in both numerator and denominator.
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}