Evaluate
\frac{\left(2t-3\right)^{2}}{t^{4}}
Expand
\frac{4t^{2}-12t+9}{t^{4}}
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4\left(t^{-1}\right)^{2}-12t^{-1}t^{-2}+9\left(t^{-2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2t^{-1}-3t^{-2}\right)^{2}.
4t^{-2}-12t^{-1}t^{-2}+9\left(t^{-2}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.
4t^{-2}-12t^{-3}+9\left(t^{-2}\right)^{2}
To multiply powers of the same base, add their exponents. Add -1 and -2 to get -3.
4t^{-2}-12t^{-3}+9t^{-4}
To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.
4\left(t^{-1}\right)^{2}-12t^{-1}t^{-2}+9\left(t^{-2}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2t^{-1}-3t^{-2}\right)^{2}.
4t^{-2}-12t^{-1}t^{-2}+9\left(t^{-2}\right)^{2}
To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.
4t^{-2}-12t^{-3}+9\left(t^{-2}\right)^{2}
To multiply powers of the same base, add their exponents. Add -1 and -2 to get -3.
4t^{-2}-12t^{-3}+9t^{-4}
To raise a power to another power, multiply the exponents. Multiply -2 and 2 to get -4.
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}