Question 717520
Your question, in simpler terms, is: What is {{{-x^2}}} when x = -1?<br>
The answer requires that we understand a fundamental fact about exponents: Exponents apply only to what is immediately in front of them. ("Immediately in front" means literally "the very first character to the left of"<ul><li>If a digit (0-9) is immediately in front of the exponent, the exponent applies only to the number which that digit is the last/only digit. Important: If there is a "-" in front of this number, the exponent does <u>not</u> apply to it! For example:
{{{-10^2}}} means -(10*10) which equals -100 (<u>not</u> (-10)(-10) which equals 100.</li><li>If a variable is immediately in front of an exponent, the exponent applies only to that variable, not to any other variables or numbers which may precede that variable. For example, {{{24xy^3}}} means 24*x*y*y*y.</li><li>If a end-of-a-group symbol (like "}" or "]" or "}") is immediately in front of an exponent, it applies to the entire grouped expression. For example, {{{(x^2-4x+3)^3}}} means {{{(x^2-4x+3)*(x^2-4x+3)*(x^2-4x+3)}}} but {{{x^2-4x+3^3}}} means just {{{x^2-4x+3*3*3}}}</li></ul>The way exponents work like this is another reason it is a good idea to use parentheses when making substitutions. If you substitute a -1 into {{{x^2}}} with parentheses you get:
{{{(-1)^2 = (-1)*(-1) = 1}}}
Without the parentheses we would have:
{{{-1^2 = -1*1 = -1}}}<br>
Finally we'll answer your question, if you haven't figured it out already. {{{-x^2}}} when x = -1:
{{{-(-1)^2 = -(-1)*(-1) = -1}}}