Can I use the power rule?

Question

Can I use the rule of powers to calculate this:

2*sqrt(a^5) - a*sqrt(a^3)

Thank you.

Answer 1

yes

2 sqrt (a^5) - a sqrt(a^3) =
2 a^(5/2) - a^(5/2) =
a^(5/2)

Answer 2

2 sqrt (a^4*a) - a sqrt (a^2*a)
= 2a^2 sqrt a - a^2 sqrt a
= (2a^2 - a^2) * sqrt a
= a^2 * sqrt a

Answer 3

yes you can.

X * a ^ (p/q) - Y * a^(p/q) = (X-Y)*a^(p/q)

note that sqrt(a) = a^(1/2)
and [ sqrt(a) ] ^ 3 = a^(3/2)

Answer 4

2√(a^5) = 2√(a^4•a) = 2a²√a
a√(a^3) = a√(a²•a) = a²√a

[√(a²) = |a|, not a, unless you've already agreed that you're working with a ≥ 0. every Alg 2 book shows you this then right away agrees to ignore it]

so you have 2a²√a - a²√a = a²√a

Answer 5

no this problem must be solver using the tantanka method....and by the way the answer is 6squared