# Simplify a) and b). Round your answer to c) properly to four decimal places. Use the ^ symbol to indicate exponents where necessary a)(t^6)^(1/2) b)(n^0.5)^(8) c)o.65^(-1/2)

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Simplify.

a) `(t^6)^(1/2)`

Raising a power to anoher power, multiply the powers together.

`t^(6*(1/2))`

**The solution for a is `t^3.`**

b) `(n^0.5)^8`

Using the same rule, yields, `n^(0.5*8)`

**The solution for b is `n^4.`**

c) `0.65^(-1/2)`

`(0.65^(1/2))^-1`

`(sqrt(.65))^-1`

`1/(sqrt(.65))` = `1.2403`

**The solution to c is 1.2403**

a. `(t^6)^(1/2)=t^(6xx1/2)=t^(3)`

Since

`(x^m)^n=x^(mxxn)=x^(mn)`

b. `(n^0.5)^8=n^(0.5xx8)=n^4`

`` c. `0.65^(-1/2)=1/(.65^(1/2))`

`=1/.806225774`

`=1.240347`

`approx1.2403`