Question

(64/25) raised to -3/2

Answer 1

Step-by-step explanation:

:

64 Simplify —— 25

Equation at the end of step1:

64 ——)2) ÷ 3 25

STEP2:

 2.1   Negative number raised to an even power is positive

For example let's look at (-7)6 , where (-7) , a negative number, is raised to 6 , an even exponent :

(-7)6 can be written as (-7)•(-7)•(-7)•(-7)•(-7)•(-7)

Now, using the rule that says minus times minus is plus, (-7)6 can be written as (49)•(49)•(49) which in turn can be written as (7)•(7)•(7)•(7)•(7)•(7) or 76 which is positive.

We proved that (-7)6 is equal to (7)6 which is a positive number

Using the same arguments as above, replacing (-7) by any negative number, and replacing the exponent 6 by any even exponent, we proved which had to be proved

 2.2     64 = 26 (-64)2 = (26)2 = 212  2.3     25 = 52 (25)2 = (52)2 = 54

Equation at the end of step2:

212 ——— ÷ 3 54

STEP3:

212 Divide ——— by 3 54

Final result :

4096 ———— = 2.18453 1875