Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression. (a) (e-3)2/3 (b) e^4/e^-1/2 (c) (e-2)-4 (d) (e-4)(e-3/2)

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asked Jan 16, 2021 210k views

1 Answer

Borisdonchev · Answer 1 · 2021-01-20T19:52:47+0000

Answer:

$1.~e^(-2) \\2.~e^{(7)/(2)}\\3.~e^8\\4.~e^{(-11)/(2)}$

Explanation:

We have to simplify the given exponential exponents.

Exponential Properties:

$e^0 =1\\e^a.e^b = e^(a+b)\\\\\displaystyle(e^a)/(e^b) = e^(a-b)\\\\(e^a)^b = e^(ab)\\\\e^(-a) = (1)/(e^a)$

Simplification takes place in the following manner:

a)

$(e^(-3))^(2)/(3)\\(e^a)^b = e^(ab)\\=e^{-3* (2)/(3)}\\=e^(-2)$

b)

$(e^4)(e^{(-1)/(2)})\\e^a.e^b = e^(a+b)\\=e^{(4+(-1)/(2))} \\= e^{(7)/(2)}$

c)

$(e^(-2))^(-4)\\(e^a)^b = e^(ab)\\= e^(-2* -4)\\=e^8$

d)

$(e^(-4))(e^{(-3)/(2)})\\e^a.e^b = e^(a+b)\\=e^{(-4+(-3)/(2))} \\= e^{(-11)/(2)}$