Question

Simplify 3√875x⁵y⁹

Answer 1

5∛7 ×
`x^(5/3)` × y³ is answer.

Explanation:

we have to simplify the given expression 3√875x⁵y⁹

we use exponent rule for radical
`\sqrt[n]{xy} = \sqrt[n]{x} \sqrt[n]{y}`

we use this rule is this expression

3√875x⁵y⁹ = ∛875 × ∛x⁵ × ∛y⁹

∛875 = ∛125 ×7 = 5 ∛ 7

using exponent rule for radical
`\sqrt[n]{x^(m)}=x^(m/n)` we get

`\sqrt[3]{x^(5) } =x^(5/3)`

similarly

`\sqrt[3]{y^(9) } = y^(9/3)`

putting these values in given expression we get

3√875x⁵y⁹ = 5∛7 ×
`x^(5/3)` × y³

therefore, our expression simplifies to 5∛7 ×
`x^(5/3)` × y³.

Answer 2

`5\sqrt[3]{7}*y^3*x^{(5)/(3)}`

Explanation:

We are asked to simplify the radical expression:
`\sqrt[3]{875x^5y^9}`.

Using exponent rule for radical
`\sqrt[n]{ab} =\sqrt[n]{a}*\sqrt[n]{b}` we can rewrite our expression as:

`\sqrt[3]{875x^5y^9}=\sqrt[3]{875}*\sqrt[3]{x^5}*\sqrt[3]{y^9}`

`\sqrt[3]{875}=\sqrt[3]{125*7}=5\sqrt[3]{7}`

Using exponent rules for radical
`\sqrt[n]{a^m}=a^(m)/(n)` we will get,

`\sqrt[3]{x^5}=(x^5)^{(1)/(3)}=x^{(5)/(3)}`

Using exponent rules for radical
`\sqrt[n]{a^m}=a^(m)/(n)` we will get,

`\sqrt[3]{y^9}=(y^9)^3=y^{(9)/(3)}=y^3`

Upon substituting these values in our expression we will get,

`\sqrt[3]{x^5}*\sqrt[3]{y^9}=5\sqrt[3]{7}*x^{(5)/(3)}*y^3`

Therefore, our radical expression simplifies to
`5\sqrt[3]{7}*y^3*x^{(5)/(3)}`.