SOLUTION: 2^31*4^31*5^62*7^31*8^93=y When I tried to solve the problem using an online calculator and got strange results. For example, I entered eight to the ninety-third power and got,

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 2^31*4^31*5^62*7^31*8^93=y When I tried to solve the problem using an online calculator and got strange results. For example, I entered eight to the ninety-third power and got,      Log On


   

Question 75098: 2^31*4^31*5^62*7^31*8^93=y
When I tried to solve the problem using an online calculator and got strange results. For example, I entered eight to the ninety-third power and got, 9.713344461128645e+83 as an answer which is a format I am unable to work further with. Thanks for your help!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Simplify:

2%5E31%2A4%5E31%2A5%5E62%2A7%5E31%2A8%5E93=y

Notice that all the exponents are multiples
of 31.

Write the 62 power as 2%2A31

and write the 93 power as 3%2A31

2%5E31%2A4%5E31%2A5%5E%282%2A31%29%2A7%5E31%2A8%5E%283%2A31%29=y

Now write the 5%5E%282%2A31%29 as %285%5E2%29%5E31

and write the 8%5E%283%2A31%29 as %288%5E3%29%5E31

+2%5E31%2A4%5E31%2A%285%5E2%29%5E31%2A7%5E31%2A%288%5E3%29%5E31=y+

Now write the 5%5E2 as 25
and write the 8%5E3 as 512

+2%5E31%2A4%5E31%2A25%5E31%2A7%5E31%2A512%5E31=y+

Now since all factors are raised to the 31 power,

we can write the above as:

+%282%2A4%2A25%2A7%2A512%29%5E31=y+

Then finally multiply the numbers in the
parentheses and you end up with

+%28102400%29%5E31=y+

or

102400%5E31=y

and you would just leave the answer like
that because that number written out
would have hundreds of digits.

Edwin