I have a question about exponents of rational expressions.
I have two answers for one problem. One was written on a university mathlab and the other from a calculator.
(3a^3/2)*(-7a^1/5) = -21a^17/10
(3a^3/2)*(-7a^1/5) = -21^a4/10
Can you tell me which is right?
The first one looks right to me based on the multiplication of fractions.
the first one is definitely the right one.
when you add the exponents 3/2 + 1/5
you get 17/10
Thank you. I don't what to talk in class like I haven't done my homework. I did, but the two answers confused me. The second looked plausible, but I trust a university mathlab a whole lot more.
To determine which answer is correct, let's simplify the expression step by step using the rules of exponents.
Given expression: (3a^(3/2))*(-7a^(1/5))
Step 1: Apply the rule of multiplying same bases with different exponents.
The coefficients (3 and -7) can be multiplied together: 3 * -7 = -21.
Step 2: Multiply the variables together, keeping the base the same (a).
The exponents (3/2 and 1/5) can be added together: (3/2) + (1/5) = 17/10.
Note: When adding fractions, a common denominator is needed.
Therefore, based on the above steps, the correct answer is:
(3a^(3/2))*(-7a^(1/5)) = -21a^(17/10).
The second answer you provided, -21^a^(4/10), appears to have a typographical error. It should be written as -21a^(4/10) for the exponent part. But even so, it does not match the correct answer -21a^(17/10).
Therefore, the first answer you mentioned, -21a^(17/10), is correct based on the rules of exponents.