Answer:
x^-2 = 1/4
x^-1 = -1/2
x^0 = 1
x^1 = -2
x^2 = 4
Step-by-step explanation:
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The values for the given items by evaluating x = -2
[tex]x^-^2=\frac{1}{4}[/tex]
[tex]x^-^1=-\frac{1}{2}[/tex]
[tex]x^0=1[/tex]
[tex]x^1=-2[/tex]
[tex]x^2=4[/tex]
These values are calculated by substituting x = -2 in the given expressions.
Exponents, also known as powers, are values that show how many times to multiply a base number by itself.
example: [tex]2^{4}[/tex] = 2 × 2 × 2 × 2
Here the base is 2 and the power is 4
Powers are all the real numbers. Thus, in the case of negative powers, it follows the exponential law: [tex]a^-^n=\frac{1}{a^n}[/tex]
it is given that x = -2
On substituting in the given expressions,
[tex]x^-^2=(-2)^-^2[/tex]
⇒ [tex]\frac{1}{-2 . -2} =\frac{1}{4}[/tex]
[tex]x^-^1=(-2)^-^1[/tex]
⇒ [tex]\frac{1}{-2}[/tex]
[tex]x^0=(-2)^0[/tex]
⇒ [tex]x^0=1[/tex]
[tex]x^1=(-2)^1[/tex]
⇒ [tex]x^1=-2[/tex]
[tex]x^2=(-2)^2[/tex]
⇒ [tex](-2).(-2)=4[/tex]
Therefore, match the following for the given items by evaluating the expression for x = -2 is:
[tex]x^-^2=\frac{1}{4}[/tex]
[tex]x^-^1=-\frac{1}{2}[/tex]
[tex]x^0=1[/tex]
[tex]x^1=-2[/tex]
[tex]x^2=4[/tex]
Learn more about exponential laws here:
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