Question

Which expression is equivalent to 3/56x^7y^5 , if x ≠0 and y≠0

Answer 1

Answer:

$2x^2y\sqrt[3]{7xy^2}$

Step-by-step explanation:

Given

$\sqrt[3]{56x^7y^5}$

Required

Solve

Expand

$\sqrt[3]{8*7*x^6*x*y^3*y^2}$

Rewrite as:

$\sqrt[3]{8*x^6*y^3*7*x*y^2}$

Split

$\sqrt[3]{8*x^6*y^3} *\sqrt[3]{7*x*y^2}$

Express 8 as 2^3

$\sqrt[3]{2^3*x^6*y^3} *\sqrt[3]{7*x*y^2}$

Apply law of indices

$2^{(3/3)}*x^{(6/3)}*y^{(3/3)} *\sqrt[3]{7*x*y^2}$

$2*x^2*y *\sqrt[3]{7*x*y^2}$

$2x^2y *\sqrt[3]{7xy^2}$

$2x^2y\sqrt[3]{7xy^2}$