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# If a negative number is in parenthesis and has a positive exponent, how does it get a positive number outcome while a negative number withou

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If a negative number is in parenthesis and has a positive exponent, how does it get a positive number outcome while a negative number without a parenthesis and an exponent gets a negative outcome?

Aug 22, 2014

#1
+10

Consider the example (-3)2

This is really saying (-3) x (-3) = (-(-9)) = (9)

This only works for even exponets though. I'll show you with the example (-2)3

This is really saying (-2) x (-2) x (-2) = (-(-4)) x (-2) = (-(-(-8))) = (-8)

If you don't have parentheses, your basically imagining that there are parentheses after the negative sign. So, say you had -42

Aug 22, 2014

#1
+10

Consider the example (-3)2

This is really saying (-3) x (-3) = (-(-9)) = (9)

This only works for even exponets though. I'll show you with the example (-2)3

This is really saying (-2) x (-2) x (-2) = (-(-4)) x (-2) = (-(-(-8))) = (-8)

If you don't have parentheses, your basically imagining that there are parentheses after the negative sign. So, say you had -42

#2
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Thanks for that detailed explanation, ND.........this is something that gives a lot of students trouble!!!!

Maybe you should add this to "Great AnswersTo Learn From".......just a suggestion......   Aug 22, 2014
#3
+5

Aug 22, 2014
#4
+5

Yes a great explanation Ninja,   I'd like to add just a little.

people do not like the fact that  \$\$-4^2=16\$\$

the surface it appears that it should be thought of as    \$\$(-4)^2=16\$\$

\$\$But what about \$27-4^2\$ ? \\
No-one would want to interpret this as \$27+(-4)^2 = 27+16=43\$ That would be really odd.\\
Of course not \$27-4^2=27-16=11\$\\\\
so here it is really obvious that -4^2=-1*4^2=-1*16=-16\$\$

Aug 22, 2014