What is (abc)^2?

Question

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Answer 1

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.

Answer 2

Excellent answer Mona. Another way to think about this is that (abc)^2 = aabbcc

Answer 3

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.