Question

Write the expression without radicals, using only positive exponents

Answer 1

The required expression is:
`\sqrt[3]{a^2+b^2}=(a^2+b^2)^{(1)/(3)`.

Explanation:

Consider the provided expression.

`\sqrt[3]{a^2+b^2}`

Now use the property:
`\sqrt[n]{x+y}=(x+y)^{(1)/(n)}`

By using the above property the provided expression can be written as:

`\sqrt[3]{a^2+b^2}=(a^2+b^2)^{(1)/(3)`

Therefore, the required expression is:
`\sqrt[3]{a^2+b^2}=(a^2+b^2)^{(1)/(3)`.

Answer 2

`\sqrt[3]{a^(2)+b^(2)}=(a^(2)+b^(2))^{(1)/(3)}`

Explanation:

∵∛x = (x)^1/3

∴
`\sqrt[3]{a^(2)+b^(2)}=(a^(2)+b^(2))^{(1)/(3)}`

So you can replace the radicals by fractional exponents