Question

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

Answer 1

Answer: (a) $e^3$

(b) $e^{10}$

(c) $\dfrac{1}{e^4}$

(d) $e^{4}$

Step-by-step explanation:

Properties of exponents :

1) $a^m\times a^n=a^{m+n}$

2) $\dfrac{a^m}{a^n}=a^{m-n}$

3) $(a^m)^n=a^{mn}$

4) $a^{-n}=\dfrac{1}{a^n}$

Now , we simplify the given expression using the above properties.

a) $(e^6)(e^{-3})$

$=e^{6+(-3)}$   [By property (1)]

$=e^{6-3}=e^3$  [∵ (+)(-)=(-)]

b) $(e^{-2})^{-5}$

$=e^{-2\times-5}$  [By property (3)]

$=e^{10}$   [∵ (-)(-)=(+)]

c) $(\dfrac{e^6}{e^2})^{-1}$

$=(e^{6-2})^{-1}$    [By property (2)]

$=(e^{4})^{-1}$  

$=\dfrac{1}{e^4}$       [By property (4)]

d) $(e^3)^{\frac{4}{3}}$

$=e^{3\times\frac{4}{3}}$        [By property (3)]

$=e^{4}$