Given: We have the expression [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]
Step-1: [tex]\sqrt[3]{875x^{5}y^{9}}[/tex]
Step-2: [tex]\left ( 875\times x^{5} \times y^{}\right )^{1/3}[/tex] [break the cuberoot as power [tex]1/3[/tex]]
Step-3: [tex]\left ( 125.7 \right )^{1/3}\times x^{5/3}\times y^{9/3}[/tex] [break [tex]875=125\times 7[/tex]]
Step-4: [tex]\left ( 5^{3} \right )^{1/3}\times 7^{1/3}\times x^{\left ( 1+2/3 \right )}\times y^{9/3}[/tex] [ [tex]125=5^{3} \\\frac{5}{3} =1+\frac{2}{3}[/tex]]
Step-5: [tex]5^{1}\times 7^{1/3}\times x^{1}\times x^{2/3}\times y^{3}[/tex] [break the power of [tex]x[/tex]]
Step-6: [tex]5\times x\times y^{3}\left ( 7^{1/3}\times x^{2/3} \right )[/tex]
Step-7: [tex]5xy^{3}\left ( 7x^{2} \right )^{1/3}[/tex]
Step-8: [tex]5xy^{3}\sqrt[3]{7x^{2}}[/tex]
Learn more: https://brainly.com/question/20726608
