Answer:
Below is the sequence of steps which are required to follow in order to have the expression in its simplified form.
Step 1
[tex](875x^{5}y^{9})^{\frac{1}{3}}[/tex]
Step 2
[tex](125.7)^\frac{1}{3}.x^{\frac{3}{5}}.y^{\frac{9}{3}}[/tex]
Step 3
[tex](125)^{1/3}.(7)^{1/3}.x(^{\frac{3}{3}+\frac{2}{3}}).y^{3}}[/tex]
Step 4
[tex](5^{3} )^{\frac{1}{3}}.7^\frac{1}{3}.x^{(1+\frac{2}{3})}.y^{3}[/tex]
Step 5
[tex]5^{1}.7^\frac{1}{3}.x^{1}.x^\frac{2}{3}.y^3[/tex]
Step 6
5xy³([tex]7^{\frac{1}{3} }[/tex][tex]x^{\frac{2}{3} }[/tex])
Step 7
5xy³([tex]7x^{2}[/tex])[tex]\frac{1}{3}[/tex]
Step 8
5xy³[tex]\sqrt[3]{7x^{2}}[/tex]
