Question

Help, hurry up please

Answer 1

The correct answer is second option

(√x²/⁷)(√y⁵/³)

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)

Answer 2

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