(-e^-t)^2 = e^(-2t) It could also be written as : 1/e^(2t)
Start by noticing the whole value is negative: a negative squared becomes positive: so we know our answer will be positive something Then look at the rest of the problem (e^-t)^2 since the 2 is on the outside of the parentheses your two powers will be multiplied together giving you: e^(-2t) (That is a property of powers (a^x)^y becomes a^(xy) so your final answer is +e^(-2t) It’s always hard to put math into words, but try to just follow the steps. I hope this helped!
(-e^-t)² Distribute the square to the negative and the e: (-1)²(e^-t)² -1 squared becomes 1 and disappears. When taking a power to another power, simply multiply exponents: =e^(-2t)
e^-2t Any power raised to another power is simply the number raised to the multiple of the powers. i.e. (x^y)^z = x^(y*z) Also, you can split numbers that are multiplied together and raise them to the same power individually. i.e. (x*y)^z = x^z * y^z So putting that together, you get (-1*e^-t)^2 = (-1)^2 * (e^-t)^2, which equals (-1)^2 * e^(-2t) -1 squared = 1 Answer: e^(-2t)
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