Question

Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.

Answer 1

Answer:

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

Step-by-step explanation:

We have to simplify the given exponential exponents.

Exponential Properties:

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

Simplification takes place in the following manner:

a)

$(e^{-3})^\frac{2}{3}\\(e^a)^b = e^{ab}\\=e^{-3\times \frac{2}{3}}\\=e^{-2}$

b)

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

c)

$(e^{-2})^{-4}\\(e^a)^b = e^{ab}\\= e^{-2\times -4}\\=e^8$

d)

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