Evaluate
81y^{12}-\frac{1}{64y^{3}}
Expand
81y^{12}-\frac{1}{64y^{3}}
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3^{4}\left(y^{3}\right)^{4}-\left(4y\right)^{-3}
Expand \left(3y^{3}\right)^{4}.
3^{4}y^{12}-\left(4y\right)^{-3}
To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.
81y^{12}-\left(4y\right)^{-3}
Calculate 3 to the power of 4 and get 81.
81y^{12}-4^{-3}y^{-3}
Expand \left(4y\right)^{-3}.
81y^{12}-\frac{1}{64}y^{-3}
Calculate 4 to the power of -3 and get \frac{1}{64}.
3^{4}\left(y^{3}\right)^{4}-\left(4y\right)^{-3}
Expand \left(3y^{3}\right)^{4}.
3^{4}y^{12}-\left(4y\right)^{-3}
To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.
81y^{12}-\left(4y\right)^{-3}
Calculate 3 to the power of 4 and get 81.
81y^{12}-4^{-3}y^{-3}
Expand \left(4y\right)^{-3}.
81y^{12}-\frac{1}{64}y^{-3}
Calculate 4 to the power of -3 and get \frac{1}{64}.
Examples
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{ 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}