Evaluate
\frac{x^{3}}{4y^{5}}
Expand
\frac{x^{3}}{4y^{5}}
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\left(2\times 1y^{2}\right)^{-3}\times 2yx^{3}
Calculate x to the power of 0 and get 1.
\left(2y^{2}\right)^{-3}\times 2yx^{3}
Multiply 2 and 1 to get 2.
2^{-3}\left(y^{2}\right)^{-3}\times 2yx^{3}
Expand \left(2y^{2}\right)^{-3}.
2^{-3}y^{-6}\times 2yx^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.
\frac{1}{8}y^{-6}\times 2yx^{3}
Calculate 2 to the power of -3 and get \frac{1}{8}.
\frac{1}{4}y^{-6}yx^{3}
Multiply \frac{1}{8} and 2 to get \frac{1}{4}.
\frac{1}{4}y^{-5}x^{3}
To multiply powers of the same base, add their exponents. Add -6 and 1 to get -5.
\left(2\times 1y^{2}\right)^{-3}\times 2yx^{3}
Calculate x to the power of 0 and get 1.
\left(2y^{2}\right)^{-3}\times 2yx^{3}
Multiply 2 and 1 to get 2.
2^{-3}\left(y^{2}\right)^{-3}\times 2yx^{3}
Expand \left(2y^{2}\right)^{-3}.
2^{-3}y^{-6}\times 2yx^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.
\frac{1}{8}y^{-6}\times 2yx^{3}
Calculate 2 to the power of -3 and get \frac{1}{8}.
\frac{1}{4}y^{-6}yx^{3}
Multiply \frac{1}{8} and 2 to get \frac{1}{4}.
\frac{1}{4}y^{-5}x^{3}
To multiply powers of the same base, add their exponents. Add -6 and 1 to get -5.
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}