Answer:
216*b^2
Step-by-step explanation:
first, remember that:
a*√b = √(a^2*b)
√a*√b = √(a*b)
[tex]b^n*b^m = b^{n + m}[/tex]
[tex](b^n)^m = b^{n*m}[/tex]
Now, our expression is:
[tex]2*\sqrt{8*b^3} *9*\sqrt{18*b} = (2*9)*\sqrt{8*b^3}*\sqrt{18*b}[/tex]
Where in the right I rewrite the expression so it is easier to work.
Now we can use the second property of the above ones, to have:
[tex]18*\sqrt{8*b^3*18*b} = 18*\sqrt{(8*18)*b^{3 + 1}} = 18*\sqrt{144*b^4}[/tex]
And we know that:
[tex]\sqrt{x} = x^{1/2}[/tex]
Then:
[tex]18*\sqrt{144*b^4} = 18*(144*b^4)^{1/2} = 18*\sqrt{144}*(b^4)^{1/2}[/tex]
and 12*12 = 144, then:
[tex]18*\sqrt{144}*b^{4*1/2} = 18*12*b^2 = 216*b^2[/tex]
