MHB Rules of Exponents (4)^(1/5) * (4)^(1/5)

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The discussion clarifies the calculation of (4)^(1/5) * (4)^(1/5), confirming that it simplifies to 4^(2/5). Participants agree that both 4^(2/5) and 2^(4/5) are correct representations of the same value. The equivalence is explained by recognizing that 4 can be expressed as 2^2, leading to the conclusion that 4^(2/5) equals 2^(4/5). This highlights the concept that different forms can represent the same number in exponentiation. The conversation emphasizes understanding the underlying relationships between bases and exponents.
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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)?
 
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Yes, everything you posted is correct. (Yes)
 
MarkFL said:
Yes, everything you posted is correct. (Yes)

What is the difference between 4^(2/5) and 2^(4/5) as the answer?

How can both answers be correct?
 
RTCNTC said:
What is the difference between 4^(2/5) and 2^(4/5) as the answer?

How can both answers be correct?

They are just different form for the same number...just like 2^4 and 4^2 can both represent 16. :D
 
I hope that you know that 4= 2^2! So 4^{2/5}= (2^2)^{2/5}= 2^{4/5}.
 
Thank you everyone.
 
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