Question

79. Use properties of exponents to rewrite each expression as either an integer or as a quotient of integers p/q to show the expression is a rational number.

b. 3√54/3√2

Answer 1

See explanation below

Explanation:

First we will going to rewrite 54 into its prime factors: 54 = 3³(2)

So, the expression
`(3√(54) )/(3√(2) )` can be written as:

`(3√(3^32) )/(3√(2) ) =(3(3^(3/2))2^(1/2)  )/(3(2^(1/2)) ) =3^(3/2)=3√(3)`

*We used the fact that a square root is like having a 1/2 exponent so we multiplied the exponents inside the root by 1/2 and then simplified them*