SOLUTION: What expression raised to the fourth power is {{{81x^12y^8*2^16}}}?

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Question 83217: What expression raised to the fourth power
is 81x%5E12y%5E8%2A2%5E16?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

What expression raised to the fourth power 
is 81x%5E12y%5E8%2A2%5E16?

Let E be the required expression:

E%5E4+=+81x%5E12y%5E8%2A2%5E16

Write the 81 as 3%5E4

E%5E4+=+3%5E4x%5E12y%5E8%2A2%5E16

Solve for E by raising both sides to the 1%2F4 power


%28E%5E4%29%5E%281%2F4%29+=+%283%5E4x%5E12y%5E8%2A2%5E16%29%5E%281%2F4%29

Multiply each inner exponent by the outer exponent:

E%5E1=3%5E1x%5E3y%5E2%2A2%5E4

Erase the 1 exponents

E=3x%5E3y%5E2%2A2%5E4

Write the 2%5E4 as 16

E=3x%5E3y%5E2%2A16

Multiply the 3 by the 16

E=48x%5E3y%5E2

The desired expression is 48x%5E3y%5E2

Edwin