Question

Order the simplification steps of the expression below using the properties of rational exponents.​

Answer 1

Answer:

2, 8, 4, 6, 1, 3, 5, 7

Step-by-step explanation:

The given expression is

$\sqrt[3]{875x^5y^9}$

Using the property of radical expression.

$(875x^5y^9)^{\frac{1}{3}}$          $[\because \sqrt[3]{x}=x^{\frac{1}{3}}]$  (2nd)

Using the properties of exponents.

$(125\cdot 7)^{\frac{1}{3}}\cdot (x^5)^{\frac{1}{3}}\cdot (y^9)^{\frac{1}{3}}$          $[\because (ab)^x=a^xb^x]$

$(125\cdot 7)^{\frac{1}{3}}\cdot x^{\frac{5}{3}}\cdot y^{\frac{9}{3}}$          $[\because (x^m)^n=x^{mn}]$   (8th)

$125^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot x^{\frac{3}{3}+\frac{2}{3}}\cdot y^3$            (4th)

$(5^3)^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot x^{1+\frac{2}{3}}\cdot y^3$            (6th)

$5\cdot 7^{\frac{1}{3}}\cdot x^{1}\cdot x^{\frac{2}{3}}\cdot y^3$       $[\because x^{m+n}=x^mx^n]$     (1st)

$5\cdot x\cdot y^3\cdot (7^{\frac{1}{3}}\cdot x^{\frac{2}{3}})$          (3rd)

$5xy^3\cdot (7x^2)^{\frac{1}{3}}$        (5th)

$5xy^3\cdot \sqrt[3]{7x^2}$        (7th)

Therefore, the correct order is 2, 8, 4, 6, 1, 3, 5, 7.

Answer 2

Answer:

2, 8, 4, 6, 1, 3, 5, 7

I think this is the answer