Question

If 16^r is equivalent to 4^-1/t, what is the value of rt? A. -0.5 B. 0.5 C. -1 D. 1

Answer 1

A

Explanation:

using the rule of exponents

•
`(a^m)^(n)` =
`a^(mn)`

given

`16^(r)` ≡
`4^{(-1)/(t) }`

`(4^2)^(r)` ≡
`4^{(-1)/(t) }`

`4^(2r)` =
`4^{(-1)/(t) }`

since the bases on both sides are 4, then equate the exponents

2r =
`(-1)/(t)` ( multiply both sides by t to clear the fraction )

2rt =- 1 ( divide both sides by 2 )

rt =
`(-1)/(2)` = - 0.5