Question 220688
An important lesson to learn about exponents is that <b>an exponent applies only to what is immediately in front of it</b><br>
With {{{(-x)^2}}} it is the right parenthesis, ")", that is immediately in front of the exponent. Therefore exponent applies to the entire expression in the parentheses. So {{{(-x)^2 = (-x)(-x)}}}.<br>
With {{{-x^2}}} it is the x that is immediately in front of the exponent. Therefore the exponent applies only to the x. So {{{-x^2 = -x*x}}}<br>
Now that we understand the differences in the two expressions we can correctly evaluate them for the given values of x:
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x = 10
   {{{(-x)^2 = (-(10))^2 = (-10)^2 = (-10)*(-10) = 100}}}
   {{{-x^2 = -(10)^2 = -(10*10) = -(100) = -100}}}
x = -10
   {{{(-x)^2 = (-(-10))^2 = (10)^2 = (10)*(10) = 100}}}
   {{{-x^2 = -(-10)^2 = -((-10)*(-10)) = -(100) = -100}}}
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