Question

Match the following items by evaluating the expression for x = -6.

x^-2

x^-1

x^0

x^1

x^2

Choices:
1/36
-6
36
1
-1/6

Answer 1

Step-by-step explanation:

Put the value of x = -6 to all expressions:

`x^(-2)=(-6)^(-2)=(1)/((-6)^2)=(1)/(6)\qquad\text{used}\ a^(-n)=(1)/(a^n)\\=====================\\x^(-1)=(-6)^(-1)=(1)/((-6)^1)=-(1)/(6)\\=====================\\x^0=(-6)^0=1\qquad a^0=1\ \text{for all real numbers except 0}\\=====================\\x^1=(-6)^1=-6\qquad a^1=a\ \text{for all real numbers}\\=====================\\x^2=(-6)^2=36`

Answer 2

x^-2 matches 1/36

x^-1 matches -1/6

x^0 matches 1

x^1 matches -6

x^2 matches 36

Step-by-step explanation:

When evaluating expressions with exponents for a specific value, we simply substitute that value for x and follow the order of operations (PEMDAS). Here's the breakdown for each expression:

x^-2: (-6)^-2 = 1/(-6)^2 = 1/36

x^-1: (-6)^-1 = 1/(-6) = -1/6

x^0: (-6)^0 = 1 (any non-zero number raised to the power 0 equals 1)

x^1: (-6)^1 = -6 (any non-zero number raised to the power 1 equals itself)

x^2: (-6)^2 = (-6) * (-6) = 36

Therefore, the matches are as listed above.