Question

Simplify 3⁢√𝑎^5⁢𝑏^7⋅2⁢√5⁢𝑎^7⁢𝑏^3. Order the variables alphabetically.

Answer 1

Interpret the symbols as cube roots: ∛(a^5 b^7) · 2∛(5 a^7 b^3).

Combine the cube roots:
2∛(a^5 b^7)∛(5 a^7 b^3) = 2∛(5 a^(5+7) b^(7+3)) = 2∛(5 a^12 b^10).

Extract perfect cubes: a^12 = (a^4)^3, b^10 = (b^3)^3 · b, so
2∛(5 a^12 b^10) = 2 a^4 b^3 ∛(5 b).

Answer: 2 a^4 b^3 ∛(5 b).