Kevin P.
asked • 02/26/13...........................................
What if the question had been [(a^2)*(b^3)*c]^4?
I think the operating rule is how to deal with a power raised to another power, instead of the multiplication of the same base raised to two different powers. That says
(x^y)^z = x^(y*z)
...or we multiply the two exponents to get the final simplified power of x (because there's z copies of x^y getting multiplied together). Using numbers, (x^3)^4 would simplify to x^(3*4) = x^12.
Luke B. answered • 02/26/13
fun + learning = inevitable progress
Excellent answer Mona. Another way to think about this is that (abc)^2 = aabbcc
Mark M.
With understood multiplication, we may want to look at it more algebraically (abc)^2 = abcabc. We can then use the commutative property of real numbers with multiplication to rearrange the factors into aabbcc, which gives us Mona's answer immediately. I think this intermediate step can be important to understand, even if it's technical. I think if we follow Mona's reasoning backward, my explanation is equivalent (minus the very good note concerning exponents and multiplication, abc = (abc)^1).
02/26/13
MONA S. answered • 02/26/13
Experienced math tutor with over 9 years of experience.
abc is being used as a factor twice therefore according to the laws of exponents when we are multiplying exponents we add them. In this case abc times abc would be a^2b^2c^2. abcxabc each variable is raised to the first power so 1+1 equals 2 and therefore the exponent is equal to 2 and you do this for each variable.
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MONA S.
Thank you. That is an excellent way to rewrite the question. Thank you for sharing that way of presenting it with me.
02/26/13