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how do I know what exponent and base I use when I simplify an exponent, for example, 16^1/4 become (2^4)^1/4 which becomes 2. How do I know I have to use 2^4 instead of another number like 4^2 that is still equal to 16. Why can't I use a different number that is equal to the same thing?

User Limp
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1 Answer

6 votes

Answer:

Reason:

16^1/4=(2^4)^1/4

Step-by-step explanation:

You can use either 4^2 or 2^4 both gives the same answer.

In order to simplify the steps we use 2^4.

we get,


16^{(1)/(4)^{}^{}}=(2^4)^{(1)/(4)}
=2^{4*(1)/(4)}

4 in the power got cancelled and we get,


=2

Alternate method:

If we use 4^2 we get,


16^{(1)/(4)}=(4^2)^{(1)/(4)}
=4^{2*(1)/(4)}
=4^{(1)/(2)}

we use 4=2^2,


=(2^2)^{(1)/(2)}=2

In order to get answer quicker we appropiately use 2^4=16 here.

Rules in exponent:


a^n* a^m=a^(n+m)
(a^n)/(a^m)=a^(n-m)
(1)/(a^m)=a^(-m)
(a^n)^m=a^(n* m)
4^{3*(1)/(2)}=4^{(3)/(2)}

use 4=2^2, we get


=2^{2*(3)/(2)}

2 got cancelled in the power, we get


=2^3
=8

we get,


4^{3*(1)/(2)}=8

User CaTourist
by
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