Question

if powers are same then bases are also same?
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Answer 1

Answer:-

No, we would not be completely correct if we say that if powers are same then the bases are also same.

As in the que:-

The power of x and y is same which is 5 but we dont have any defined value of x and y, but if we would have,

$\bf\leadsto x\cancel{^5} = y\cancel{^5}\ \ \ \ \textrm{Then we can say that x = y.}$

But is the above statement is true for all conditions??

• Well its not, the above statement is not correct for all conditions, for example let us take x be 4 and y be -4 and their power be 2.

For x:-

$\underline{\bf\mapsto{\underline{ 4^2 = 4\times4 = 16.}}}.....(1)$

For y:-

$\underline{\bf\mapsto{\underline{(-4)^2 = (-4)\times(-4) = 16.}}}.....(2)$

So From (1) And (2) we get:-

$\tt\mapsto 16 = 16.\\ \\ \tt\mapsto 4\cancel{^2} = (-4)\cancel{^2}.\\ \\ \bf\mapsto 4 = -4.$

But we know that $\bf 4\neq -4.$

So we can Say that the above statement that is if $\bf x^5 = y^5$ then x = y is only possible for positive values.