Question

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

Answer 1

Answer:

2 is the exponent

Step-by-step explanation:

Given is an equation as

$\frac{64}{81} =(\frac{8}{9} )^m$

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

$\frac{64}{81} =(\frac{8^2}{9^2} )\\\frac{64}{81} =(\frac{8}{9} )^2$

Comparing m =2

Answer 2

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