Question

64/81=(8/9) what is the exponent

Answer 1

Hi

x = exponent

64 = 8·8 = 8^2
81 = 9·9 = 9^2

64/81 = 8^2/9^2 = (8/9)^2

(8/9)^2 = (8/9)^x

x = 2

Answer: The exponent is 2

Answer 2

2 is the exponent

Explanation:

Given is an equation as

`(64)/(81) =((8)/(9) )^m`

and we have to find the exponent m

Since 64 and 81 are prime to each other we cannot simplify the fraction.

We find that both 64 and 81 are perfect squares of 8 and 9 respectively

Hence we write

`(64)/(81) =((8^2)/(9^2) )\\(64)/(81) =((8)/(9) )^2`

Comparing m =2