Question

Applying properties of Exponents in exercise,use the properties of exponents to simplify the expression.See example 1.

(a) (52)(53)
(b) (52)(5-3)
(c) (52)2
(d) 5-3

Answer 1

Answer: a) 15625, b) 0.2, c) 625, d) 0.008.

Explanation:

Since we have given that

a)
`(5^2)(5^3)`

As we know that

`a^m* a^n=a^(m+n)`

So, it becomes,

`5^2* 5^3=5^(2+3)=5^6=15625`

(b)
`(5^2)(5^(-3))`

So, it becomes,

`5^2* 5^(-3)=5^(2-3)=5^(-1)=(1)/(5)=0.2`

(c)
`(5^2)^2`

As we know that

`(a^m)^n=a^(mn)`

So, it becomes,

`5^(2* 2)=5^4=625`

(d)
`5^(-3)`

`a^(-m)=(1)/(a^m)\\\\5^(-3)=(1)/(5^3)=(1)/(125)=0.008`

Hence, a) 15625, b) 0.2, c) 625, d) 0.008.