kp1811 wrote:

Is \((4^x)^{(5-3x)}=1\)?

(1) x is an integer.

(2) The product of x and positive integer y is not x.

First of all \((4^x)^{(5-3x)}=4^{x*(5-3x)}\)

This expression to be equal to \(1\), \(x*(5-3x)\) must be equal to \(0\).

\(x*(5-3x)=0\), \(x=0\)or \(x=\frac{5}{3}\).

So basically the question asks is \(x=0\) or \(x=\frac{5}{3}\).

(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.

(2) \(xy\neq{x}\), hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.

(1)+(2) x is an integer but not 0. So x is not 0, not 5/3. Hence x*(5-3x)#0, hence \((4^x)^{(5-3x)}\) does not equal to 1.

Answer: C.

Is it not possible that the expression can be equal to 1 also because 1^1=1.