What values of a and b make the equation true square root of 648 equals square root of 2^a times 3^b

In symbols, sqrt(648) = 2^a * 3^b.

One way in which to tackle this is to factor *648.

648 = 81*8.

Note that 81 = 3^4 and that 8 = 2^3.

Therefore, a = 4 and b = 3.

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.

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