Simplify: 6√25³ simplify : \sqrt[6]{ {25}^(3) } \\ Help help.​

Question

Simplify: 6√25³

`simplify : \sqrt[6]{ {25}^(3) } \\`
Help help.​

Answer 1

Step-by-step explanation:

Given that: ⁶√(25)³

= (25³)^1/6 {since, n√a = a^1/n}

= 25^(3*1/6) {since, (a^m)^n = a^(mn)}

In power 3 will cancel 6 in two times.

so,

= (25)^1/2 {since, 25 = 5*5 = 5²}

= (5²)^1/2 {since, (a^m)^n = a^(mn)

= 5^(2*1/2)

In power 2 wI'll cancel 2 in one time.

= 5^1 = 5

Therefore, ⁶√(25)³ = 5Ans.

Answer 2

`\\ \tt\longmapsto \sqrt[6]{25^3}`

`\\ \tt\longmapsto \sqrt[6]{(5^2)^3}`

`\\ \tt\longmapsto \sqrt[6]{5^6}`

• m√a^m=a

`\\ \tt\longmapsto 5`

Hope I helped