Answer
$50a^4b^7$
Work Step by Step
RECALL:
(1) $(ab)^m=a^mb^m$
(2) $(a^m)^n=a^{mn}$
Use rule (1) above to obtain:
$(2a^2b)(5ab^3)^2
\\=(2a^2b)[5^2a^2(b^3)^2]
\\=(2a^2b)[25a^2(b^3)^2]$
Use rule (2) above to obtain:
$(2a^2b)[25a^2(b^3)^2]
\\=(2a^2b)(25a^2b^{3(2)})
\\=(2a^2b)(25a^2b^{6})$
Multiply the coefficients together. Multiply the variables using the product rule for exponents $(a^m \cdot a^n=a^{m+n})$ to obtain:
$=(2\cdot 25)a^{2+2}b^{1+6}
\\=50a^4b^7$
