Question

Can someone PLZZZZ HELP!!!!

Answer 1

The solution is:

Part A.
`√(5)^{(7k)/(3)})` which is sqrt(5)^7k/3[/tex]

Part B. k = 18/7

Explanation:

Part A.

To solve this part, we're going two use THREE important properties of exponents:

1.
`(x^(n))^(m) = x^(nm)`

2.
`(x^(n))/(x^(m)) = x^(n-m)`

3.
`\sqrt[n]{x^(m)} = x^{(m)/(n) }`

Let's work the numerator using the properties 1, 2 and 3:

`(√(5)^(3) )^{(k)/(9) } }  = (√(5)^{3(k)/(9)}) = (√(5)^{(k)/(3)})`

Let's work the denominator using the properties 1, 2 and 3:

`(√(5)^(6) )^{-(k)/(3) } }  = (√(5)^{6(k)/(3)}) = (√(5)^(2k))`

Now dividing the numerator by the denominator:

`√(5)^{(k)/(3)-(-2k)})=√(5)^{(7k)/(3)})`

Part B

if
`5^{(3)/(2) } 5^{(3)/(2)} = √(5)^{(7k)/(3)})`

Then:

`5^(3) = 5^{(7k)/(6)})`

So
`(7k)/(6)} = 3`

Solving for k, we have:

k = 18/7