the rule: a^x*a^y=a^(x+y)
is only guaranteed to work when a equals a
notice: (-a)^x*a^y
-a doesn't equal a
therefore you can't add the exponents.
This is a interesting problem:
(-5)^2 * -5^3
= -5^2+3
= -5^5
Using the calculator, both (-5)^2 * -5^3 and -5^5 is -3125.
Now, consider this:
(-2)^3 * 2^5
= -2^3+5
= -2^8
Using the calculator again, we have different results:
(-2)^3 * 2^5 = -8 * 32 = -256
-2^8 = 256
The original is negative and the simplified expression is positive. It looks like the expression cannot be simplified, but why??
Please help. Thanks.
There are two things going on here. First, Quick is correct in his post, if the bases are not the same you can't add the exponents. Also, as is mentioned in another recent post when you put -2^8 in your calculator you will automatically get a positive result. Of course, with the way you intended the expression should get one in this case, but the expression -2^8 as written is -(2^8) not (-2)^8. So be careful and use parenthesis!
To get around the problem mentioned by Quick, what I would recommend is this:
(-2)^3 = (-1)^3 * 2^3 = - 2^3.
So (-2)^3 * 2^5 = (-1)^3 * 2^3 * 2^5 = -1 * 2^8 = -256.
This both allows you to simplify the problem by adding exponents, and also highlights the pesky "-" out in front.
-Dan