Question

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Order the simplification steps of the expression below using the properties of rational exponents.
\sqrt[4]{567x^{9}y^{11}}

Answer 1

The order of simplification steps of the expression using the properties of rational exponents.

\sqrt[4]{567x^{9}y^{11}} is

5 → 6 → 1 → 3 → 4 → 8 → 7 → 2

What is simplification of rational exponents?

Simplifying rational exponents involves expressing them as radicals or fractional exponents to simplify complex expressions with fractional powers.

Step 5

(567x⁹y¹¹)¹ᐟ⁴

Step 6

(81 * 7)¹ᐟ⁴ * x⁹ᐟ⁴ * y¹¹ᐟ⁴

Step 1

(81)¹ᐟ⁴ * (7)¹ᐟ⁴ * x⁽⁸ᐟ⁴⁺¹ᐟ⁴⁾ * y⁽⁸ᐟ⁴⁺³ᐟ⁴⁾

Step 3

(3⁴)¹ᐟ⁴ * (7)¹ᐟ⁴ * x⁽²⁺¹ᐟ⁴⁾ * y⁽²⁺³ᐟ⁴⁾

Step 4

3¹ * 7¹ᐟ⁴ * x² * x¹ᐟ⁴ * y² * y³ᐟ⁴

Step 8

3 * x² * y² * ( 7¹ᐟ⁴ * x¹ᐟ⁴ * y³ᐟ⁴)

Step 7

3x²y² * (7xy³)¹ᐟ⁴

Step 2

`3 {x}^(2) {y}^(2) \sqrt[4]{7x {y}^(3) }`