Question

Find the value of \[x - {y^{x - y}}\] when X=2 and Y=-2 .
A. 18
B. -18
C. 14
D. -14

Answer 1

Hint: In this polynomial equation first we will reduce the expression then we need to use the value of the indeterminates (variable) given in the question.

Complete step-by-step answer:
Given the value of X = 2 and the value of Y = -2
so , also find the expression is \[x - {y^{x - y}}\]
Now, let the given expression be capitalT
$\Rightarrow$\[T = X - {Y^{X - Y}} \to \left( 1 \right)\]
Using the bracket of equation \[\left( 1 \right)\] , we get
$\Rightarrow$\[T = \left( X \right) - {\left( Y \right)^{\left( {X - Y} \right)}}\]
Now putting the value of X = 2 in equation \[\left( 1 \right)\] , wet get
$\Rightarrow$\[T = \left( 2 \right) - {\left( Y \right)^{\left( {2 - Y} \right)}}\]
Again putting the value of Y = -2 in equation \[\left( 1 \right)\] and using the second bracket of power y ,we get
$\Rightarrow$\[T = \left( 2 \right) - {\left( { - 2} \right)^{\left\{ {2 - \left( { - 2} \right)}\right\}}}\]
Now solving power , we get
$\Rightarrow$\[T = \left( 2 \right) - {\left( { - 2} \right)^{\left( {2 + 2} \right)}}\]
$\Rightarrow$\[T = \left( 2 \right) - {\left( { - 2} \right)^{\left( 4 \right)}}\]
As the power is four so we can write
$\Rightarrow$\[T = \left( 2 \right) - \left( {2 \times 2 \times 2 \times 2} \right)\]
After the calculating
$\Rightarrow$\[T = 2 - 16\]
$\Rightarrow$\[T = - 14\]
So the value of \[T = - 14\] in equation \[\left( 1 \right)\], we get
$\Rightarrow$\[T = X - {Y^{X - Y}}\]
$\Rightarrow$\[ - 14 = T\]
$\Rightarrow$\[T = - 14\]
Therefore , the answer is -14.

Option D is the correct answer.

Note: Polynomials are the algebraic expressions that consist of variables and constant(coefficients). Variables are also called indeterminates. We cannot perform division by variable but we can generally perform the arithmetic operations such as addition, subtraction, multiplication and also positive-integer exponents for polynomial expressions and also we know that the degree of polynomial is the highest degree of a monomial within a polynomial.