Answer:
(B) 6
Step-by-step explanation:
You want the value of x in the equation ...
32^(x/3) ·32^6 = 32^8
Exponents
An exponent signifies repeated multiplication. When factors with the same base are multiplied, the number of repetitions is the sum of those in each factor. This is signified by adding the exponents.
Application
32^(x/3) · 32^6 = 32^8
The bases are the same, so the exponents add:
32^(x/3) · 32^6 = 32^(x/3+6) = 32^8
The values are equal if the exponents are equal, so we can find x using ...
x/3 +6 = 8
x/3 = 2 . . . . . . subtract 6
x = 6 . . . . . . multiply by 2
The value of x that makes the equation true is 6, choice B.
