If b is a positive integer, which of the following equals 3b^4?
A) Radical *81b^56
B) Radical 9b^8
C) Radical 9b^16
D) 9 Radical b^16
E) None of the above
well, (3b^4)^2 = 9b^8
To determine which option equals 3b^4, let's simplify each option by applying the properties of radicals:
A) Radical *81b^56
= Radical (3^4 * b^4 * b^52)
= 3b^2 * b^26
= 3b^28
B) Radical 9b^8
= Radical (3^2 * b^4 * b^4)
= 3b^2 * b^2
= 3b^4
C) Radical 9b^16
This option cannot equal 3b^4 because the power of b is 16, not 4.
D) 9 Radical b^16
This option cannot equal 3b^4 because it has an additional factor of 9.
Comparing our results, we can conclude that option B) Radical 9b^8 is the correct answer, as it equals 3b^4.