Evaluate
-\frac{1953125x^{18}y^{27}}{512}
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-\frac{1953125x^{18}y^{27}}{512}
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\left(-\frac{5}{2}x^{4}y^{3}\left(-\frac{5}{2}\right)y^{3}\left(-\frac{5}{2}\right)x^{2}y^{3}\right)^{3}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
\left(-\frac{5}{2}x^{6}y^{3}\left(-\frac{5}{2}\right)y^{3}\left(-\frac{5}{2}\right)y^{3}\right)^{3}
To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.
\left(-\frac{5}{2}x^{6}y^{6}\left(-\frac{5}{2}\right)\left(-\frac{5}{2}\right)y^{3}\right)^{3}
To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.
\left(-\frac{5}{2}x^{6}y^{9}\left(-\frac{5}{2}\right)\left(-\frac{5}{2}\right)\right)^{3}
To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.
\left(\frac{25}{4}x^{6}y^{9}\left(-\frac{5}{2}\right)\right)^{3}
Multiply -\frac{5}{2} and -\frac{5}{2} to get \frac{25}{4}.
\left(-\frac{125}{8}x^{6}y^{9}\right)^{3}
Multiply \frac{25}{4} and -\frac{5}{2} to get -\frac{125}{8}.
\left(-\frac{125}{8}\right)^{3}\left(x^{6}\right)^{3}\left(y^{9}\right)^{3}
Expand \left(-\frac{125}{8}x^{6}y^{9}\right)^{3}.
\left(-\frac{125}{8}\right)^{3}x^{18}\left(y^{9}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.
\left(-\frac{125}{8}\right)^{3}x^{18}y^{27}
To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.
-\frac{1953125}{512}x^{18}y^{27}
Calculate -\frac{125}{8} to the power of 3 and get -\frac{1953125}{512}.
\left(-\frac{5}{2}x^{4}y^{3}\left(-\frac{5}{2}\right)y^{3}\left(-\frac{5}{2}\right)x^{2}y^{3}\right)^{3}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
\left(-\frac{5}{2}x^{6}y^{3}\left(-\frac{5}{2}\right)y^{3}\left(-\frac{5}{2}\right)y^{3}\right)^{3}
To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.
\left(-\frac{5}{2}x^{6}y^{6}\left(-\frac{5}{2}\right)\left(-\frac{5}{2}\right)y^{3}\right)^{3}
To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.
\left(-\frac{5}{2}x^{6}y^{9}\left(-\frac{5}{2}\right)\left(-\frac{5}{2}\right)\right)^{3}
To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.
\left(\frac{25}{4}x^{6}y^{9}\left(-\frac{5}{2}\right)\right)^{3}
Multiply -\frac{5}{2} and -\frac{5}{2} to get \frac{25}{4}.
\left(-\frac{125}{8}x^{6}y^{9}\right)^{3}
Multiply \frac{25}{4} and -\frac{5}{2} to get -\frac{125}{8}.
\left(-\frac{125}{8}\right)^{3}\left(x^{6}\right)^{3}\left(y^{9}\right)^{3}
Expand \left(-\frac{125}{8}x^{6}y^{9}\right)^{3}.
\left(-\frac{125}{8}\right)^{3}x^{18}\left(y^{9}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.
\left(-\frac{125}{8}\right)^{3}x^{18}y^{27}
To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.
-\frac{1953125}{512}x^{18}y^{27}
Calculate -\frac{125}{8} to the power of 3 and get -\frac{1953125}{512}.
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}