Question

Help, hurry up please

Answer 1

For this case we must find an expression equivalent to:

$\frac {\sqrt [7] {x ^ 2}} {\sqrt [5] {y ^ 3}}$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So, rewriting the expression we have:

$\frac {x ^ {\frac {2} {7}}} {y ^ {\frac {3} {5}}} =$

By definition of power properties we have:

$a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}$

So:

$x ^ {\frac {2} {7}} * y ^ {- \frac {3} {5}}$

Answer:

Option A

Answer 2

Answer:

The correct answer is second option

(√x²/⁷)(√y⁵/³)

Step-by-step explanation:

Points to remember

Identities

Xᵃ * Xᵇ = x⁽ᵃ⁺ᵇ⁾

Xᵃ/Xᵇ = X⁽ᵃ⁻ᵇ⁾

1/Xᵃ = X⁻ᵃ

X¹/ᵃ = 1/Xᵃ

To find the correct option

From the figure we can see that,

7√x²/5√y³

Using identities we can write,

7√x²/5√y³ = (√x²/⁷)/(√y³/⁵

 =  (√x²/⁷) * (√y⁵/³)

Therefore the correct answer is second option

(√x²/⁷)(√y⁵/³)