Question

Match the following items by evaluating the expression for x = -2.

Answer 1

Answer:

1)¼

2)½

3)1

4)2

5)4

Step-by-step explanation:

Question-1&2:

recall that,

$\displaystyle {x}^{ - n} = \frac{1}{ {x}^{n} }$

we want to evaluate $x^{-2}$ for x=-2

to do so substitute the given value of x

$\displaystyle {2}^{ - 2}$

apply the formula:

$\displaystyle {2}^{ - 2} = \frac{1}{ {2}^{2} }$

simplify square:

$\displaystyle {2}^{ - 2} = \boxed{\frac{1}{ 4} }$

likewise substitute the given value of x to x^-1:

$\displaystyle {2}^{ - 1}$

apply the formula:

$\displaystyle {2}^{ 1} = \frac{1}{ {2}^{1} }$

$\displaystyle {2}^{ 1} = \boxed{\frac{1}{ {2}^{} } }$

Question-3:

substitute the value of x

$\displaystyle {2}^{ 0}$

it's a universal truth that x⁰=1 Thus

$\displaystyle \boxed{1}$

Question-4&5:

Substitute the given value of x to x¹ and x² respectively

$\displaystyle {2}^{ 1} \quad \bigg | \quad {2}^{2}$

simplify:

$\displaystyle \boxed{2} \quad \bigg | \quad \boxed4$

and we're done!

Answer 2

Answer:

see below

Step-by-step explanation:

x^-2 = 1/x^2  Let x = -2      1/ (-2)^2 = 1/4

x^-1 = 1/x^1  Let x = -2      1/ (-2)^1 = 1/(-2) = -1/2

x^0 = 1  

x^1 = x  Let x = -2      (-2)

x^2 =   Let x = -2      (-2)^2 = 4