- #1
mathdad
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Rules of Exponents
(4)^(1/5) * (4)^(1/5)
4^(1/5) + (1/5)
4^(2/5)
Correct?
Is the answer 2^(4/5)?
(4)^(1/5) * (4)^(1/5)
4^(1/5) + (1/5)
4^(2/5)
Correct?
Is the answer 2^(4/5)?
MarkFL said:Yes, everything you posted is correct. (Yes)
RTCNTC said:What is the difference between 4^(2/5) and 2^(4/5) as the answer?
How can both answers be correct?
The rule for exponents when multiplying two terms with the same base is to add the exponents together. In this case, (4)^(1/5) * (4)^(1/5) would become (4)^(1/5 + 1/5) which simplifies to (4)^(2/5).
The exponent of 1/5 means that the base will be multiplied by itself 1/5 times. In other words, it is the fifth root of the base.
Yes, the exponent can be a fraction. This is known as a rational exponent and it represents the root of the base. In this case, the fifth root of 4.
The value of (4)^(1/5) * (4)^(1/5) is (4)^(2/5) which is approximately 1.3195.
To simplify this expression, you can use the rule for exponents when multiplying with the same base, which is to add the exponents together. In this case, (4)^(1/5) * (4)^(1/5) becomes (4)^(1/5 + 1/5) which simplifies to (4)^(2/5).