Answer:
Number the boxes on the left 1–8 from top to bottom. Then their correct order on the right is 3, 7, 8, 4, 6, 5, 2, 1
Explanation:
Trade the cube root for a 1/3 power:
(875x^5y^9)^(1/3)
Distribute the 1/3 power:
(125·7)^(1/3)·x^(5/3)·y^(9/3)
Further distribute the powers, rewrite the improper fractions:
125^(1/3)·7^(1/3)·x^(3/3+2/3)·y^3
Write 125 as a cube and simplify 3/3:
(5^3)^(1/3)·7^(1/3)·x^(1+2/3)·y^3
Simplify the cube root of a cube and the x term:
5·7^(1/3)·x·x^(2/3)·y^3
Group the terms with fractional exponents:
5·x·y^3·(7^(1/3)·x^(2/3))
Factor out the 1/3 exponent:
5xy^3·(7x^2)^(1/3)
Trade the 1/3 exponent for a cube root symbol:
5xy^3·∛(7x^2)