- 0,5 x ^ { 2 } y ^ { 2 } \cdot ( - 2 x ^ { 3 } y ) =
Evaluate
y^{3}x^{5}
Differentiate w.r.t. x
5y^{3}x^{4}
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\left(-0,5\right)^{1}x^{2}y^{2}\left(-2\right)^{1}x^{3}y^{1}
Use the rules of exponents to simplify the expression.
\left(-0,5\right)^{1}\left(-2\right)^{1}x^{2}x^{3}y^{2}y^{1}
Use the Commutative Property of Multiplication.
\left(-0,5\right)^{1}\left(-2\right)^{1}x^{2+3}y^{2+1}
To multiply powers of the same base, add their exponents.
\left(-0,5\right)^{1}\left(-2\right)^{1}x^{5}y^{2+1}
Add the exponents 2 and 3.
\left(-0,5\right)^{1}\left(-2\right)^{1}x^{5}y^{3}
Add the exponents 2 and 1.
x^{5}y^{3}
Multiply -0,5 times -2.
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}