PLease help with this problem. My friend and I differ on answer.
(3abc^2 )^4/(7a^2 b)^4 =
81c^8/2401a^4.'
There may be a factor for 81 and 2401 but it isn't obvious if there is one.
thank you very much, my friend was right I was wrong
2401 = 7*7*7*7
81 = 3*3*3*3
There are no common factors
To simplify the given expression, we can follow the order of operations, which is known as BEDMAS (or PEMDAS in some regions).
First, let's simplify the numerator of the expression: (3abc^2)^4.
To raise a power to another power, we multiply the exponents. Thus, we get:
(3^4) * (a^4) * (b^4) * (c^2)^4 = 81a^4b^4c^8
Now, let's simplify the denominator of the expression: (7a^2b)^4.
Again, using the exponent rule, we have:
(7^4) * (a^2)^4 * (b^4) = 2401a^8b^4
Now that we have simplified the expression into its numerator and denominator, we can divide them:
81a^4b^4c^8 / 2401a^8b^4
To divide, we can subtract the exponents of the like terms:
= (81/2401) * (1/a^4) * (c^8/1)
= (81/2401) * (c^8/a^4)
So, the simplified expression is (81/2401) * (c^8/a^4).
Now, please note that whether your friend agrees or not depends on the specific answer they arrived at and why they believe it is correct. If they have a different approach or have misunderstood the problem, it is essential to have a discussion to clarify any discrepancies.