Question

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

(a) (54)(252)
(b) (91/3)(31/3)
(c) (1/3)^-3
(d) (64)(6- 5)

Answer 1

(a)
`5^(8)`

(b) 3

(c) 27

(d)
`(1)/(6)`

Explanation:

We need simplify the given expressions.

(a)

Consider the given expression is

`(5^4)(25^2)`

`(5^4)((5^2)^2)`

Using the properties of exponents we get

`(5^4)(5^4)`
`[\because (a^m)^n=a^(mn)]`

`5^(4+4)`
`[\because a^ma^n=a^(m+n)]`

`5^(8)`

(b)

Consider the given expression is

`(9^{(1)/(3)})(3^{(1)/(3)})`

`((3^2)^{(1)/(3)})(3^{(1)/(3)})`

Using the properties of exponents we get

`(3^{(2)/(3)})(3^{(1)/(3)})`
`[\because (a^m)^n=a^(mn)]`

`3^{(2)/(3)+(1)/(3)}`
`[\because a^ma^n=a^(m+n)]`

`3^(1)`

`3`

(c)

Consider the given expression is

`((1)/(3))^(-3)`

Using the properties of exponents we get

`((3)/(1))^(3)`
`[\because a^(-n)=(1)/(a^n)]`

`3^(3)`

`27`

(d)

Consider the given expression is

`(6^4)(6^(-5))`

Using the properties of exponents we get

`6^(4+(-5))`
`[\because a^ma^n=a^(m+n)]`

`6^(-1)`

`(1)/(6^(1))`
`[\because a^(-n)=(1)/(a^n)]`

`(1)/(6)`