Exponents question

[PocketRocket]

How did we know not to multiply 32 x 1/5 which would not give you the power of 2 but 6.4 ? I thought that when its "power to the power of" you just multiply the two

What am I missing here? thanx

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[FeralisExtremum]

Think of it this way: the powers have to be on the same "level" to be multiplied together. 10^32^(1/5) is the base number and 2 different tiers of exponents. But in 10^(2^5)^1/5), the 5 and 1/5 are actually on the same level of exponent, although the image doesn't quite make that clear. You can't multiply 32 and 1/5th for the same reason that in a problem like 3^2 you don't multiple 3 and 2 to get your answer.

 

[PocketRocket]

ohhhhhh gotchu, so it would have to have been (10^32)^(1/5) for me to multiply the powers like that. Thank you!

 

[DAT Destroyer]

View attachment 191629
How did we know not to multiply 32 x 1/5 which would not give you the power of 2 but 6.4 ? I thought that when its "power to the power of" you just multiply the two

What am I missing here? thanx

Pay close attention to the parentheses. Your way will be correct it it were: (10^32)^(1/5).

The question is 10^(32)^(1/5) = 10^(2^5)^(1/5) = 10^2 = 100