What expressions are equivalent to 5 to the power of 2 divided by 5 to the power of 8

Answer 1

Your initial expression looks like 5²/5⁸. Since both bases are alike, you can use the division rule for the exponents (subtract them). You'll get 5^-6 which is the same as 1/5⁶.

The expression expands to 5•5/(5•5•5•5•5•5•5•5), the top two 5's cancel out two of the bottom 5's, so you're left with 1•1/(5•5•5•5•5•5), or 1/5⁶, as above. You could calculate out 1/5⁶ to get the fractional form (1/15,625) or decimal form (0.000064) if you wish.

Answer 2

5^2/5^8

= 5^(2-8)

= 5^-6

= 1/5^6

=1/5(5)(5)(5)(5)(5)

= 1/25(25)(25)

= 1/625(25)

= 1/15,625

= 0.000064

= 64/1,000,000

=64 millionths

= 1/millionth times 64

= 25/5^8

= 25/3,906

=5^2/3,906

among other expressions with the same value

UNLESS, by chance, you really meant to write (although it's not written that way, given PEMDAS order of arithmetic operations)

then

{5^2)/5]^8 = [5 to the power of 2) divided by 5] all raised to the 8th power

then you get 5^16/5^8 = 5^8 = 390,625

or maybe you may even have meant to write

[5^(2/5)]^8 = (5^16/5^40) = 5^-24 = 1/5^24 = about 1/5.96464478x10^16

You might check how the original problem was written, just in case. A copying error could throw the answer off, a lot.

Answer 3

5² / 5⁸ = 5^2-8 = 5^-6 = 1/(5·5·5·5·5·5)