Evaluate
\frac{1}{y^{12}x^{20}z^{24}}
Expand
\frac{1}{y^{12}x^{20}z^{24}}
Share
Copied to clipboard
\left(y^{6}x^{10}z^{12}\right)^{-2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(y^{6}\right)^{-2}\left(x^{10}\right)^{-2}\left(z^{12}\right)^{-2}
Expand \left(y^{6}x^{10}z^{12}\right)^{-2}.
y^{-12}\left(x^{10}\right)^{-2}\left(z^{12}\right)^{-2}
To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.
y^{-12}x^{-20}\left(z^{12}\right)^{-2}
To raise a power to another power, multiply the exponents. Multiply 10 and -2 to get -20.
y^{-12}x^{-20}z^{-24}
To raise a power to another power, multiply the exponents. Multiply 12 and -2 to get -24.
\left(y^{6}x^{10}z^{12}\right)^{-2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(y^{6}\right)^{-2}\left(x^{10}\right)^{-2}\left(z^{12}\right)^{-2}
Expand \left(y^{6}x^{10}z^{12}\right)^{-2}.
y^{-12}\left(x^{10}\right)^{-2}\left(z^{12}\right)^{-2}
To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.
y^{-12}x^{-20}\left(z^{12}\right)^{-2}
To raise a power to another power, multiply the exponents. Multiply 10 and -2 to get -20.
y^{-12}x^{-20}z^{-24}
To raise a power to another power, multiply the exponents. Multiply 12 and -2 to get -24.
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}