Evaluate
-9x^{6}\left(yz\right)^{3}
Expand
-9x^{6}\left(yz\right)^{3}
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2\left(-3x^{2}y\right)^{2}\left(-\frac{2}{3}\right)x^{2}yz\times \frac{3}{4}z^{2}
Multiply x and x to get x^{2}.
2\left(-3x^{2}y\right)^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
2\left(-3\right)^{2}\left(x^{2}\right)^{2}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
Expand \left(-3x^{2}y\right)^{2}.
2\left(-3\right)^{2}x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
2\times 9x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
Calculate -3 to the power of 2 and get 9.
18x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
Multiply 2 and 9 to get 18.
-12x^{4}y^{2}x^{2}yz^{3}\times \frac{3}{4}
Multiply 18 and -\frac{2}{3} to get -12.
-12x^{6}y^{2}yz^{3}\times \frac{3}{4}
To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.
-12x^{6}y^{3}z^{3}\times \frac{3}{4}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
-9x^{6}y^{3}z^{3}
Multiply -12 and \frac{3}{4} to get -9.
2\left(-3x^{2}y\right)^{2}\left(-\frac{2}{3}\right)x^{2}yz\times \frac{3}{4}z^{2}
Multiply x and x to get x^{2}.
2\left(-3x^{2}y\right)^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
2\left(-3\right)^{2}\left(x^{2}\right)^{2}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
Expand \left(-3x^{2}y\right)^{2}.
2\left(-3\right)^{2}x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
2\times 9x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
Calculate -3 to the power of 2 and get 9.
18x^{4}y^{2}\left(-\frac{2}{3}\right)x^{2}yz^{3}\times \frac{3}{4}
Multiply 2 and 9 to get 18.
-12x^{4}y^{2}x^{2}yz^{3}\times \frac{3}{4}
Multiply 18 and -\frac{2}{3} to get -12.
-12x^{6}y^{2}yz^{3}\times \frac{3}{4}
To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.
-12x^{6}y^{3}z^{3}\times \frac{3}{4}
To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.
-9x^{6}y^{3}z^{3}
Multiply -12 and \frac{3}{4} to get -9.
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}