Question

For what value of x is sq 896z^15/225z^6 = xz^4/15

Answer 1

Value of x is, 8

Explanation:

Given:
`\sqrt{(896z^(15))/(225z^6)} =(xz^4)/(15) √(14z)` ,.....[1]

To find the value of x:

Using exponent rules:

• 
  `(a^n)^m = a^(nm)`

• 
  `a^n \cdot a^m = a^(n+m)`

Taking square both sides in [1] we have;

`(896z^(15))/(225z^6) = ((xz^4)/(15))^2 \cdot (14z)`

Simplify:

`(896z^(15))/(225z^6) =(x^2z^8)/(225) \cdot (14z)`

or

`(896z^(15))/(225z^6) =(14x^2z^9)/(225)`

Multiply both sides by
`(225)/(14z^9)` we get;

`x^2 = (896 z^(15))/(225z^6) * (225)/(14 z^9) = (896 z^(15))/(14 z^(9+6))`

Simplify:

`x^2 = (896 z^(15))/(14 z^(15)) = 64`

or

`x = √(64)`

Simplify:

x = 8

Therefore, the value of x is, 8