Question

Simplify (b^3)^4 times (b^2)^5 will give metal to best answer
A. b^120
B. b^2
C. b^22
D. 2b^22

Answer 1

\[(b^3)^4 \times (b^2)^5\]

Answer 2

Consider: \[2^3*2^2 = 8*4 = 32 = 3^5\]
and: \[(2^3)^2 = 8^2 = 64 = 3^6\]
This suggests, perhaps, that: \[b^n*b^m = b^{n+m}\]
and that: \[(b^n)^m = b^{nm}\]
This is in fact the case. Applying these, \[(b^3)^4 \times (b^2)^5 = b^{3\times4} \times b^{2\times5} = b^{12+10} = b^{22}\]
Thus the answer is C.

Answer 3

ok, thanks!