Question

Please help me with this math question (exponents )

please show how you solved it thank you in advance <3

Answer 1

`√(4) 3^(17)`The simplified expressions are:

`\sqrt[3]{2 \cdot \sqrt[3]{2 \cdot \sqrt[4]{2}}} = 2`

`\sqrt[4]{3^(17) + 9^(6)} = 3^(11/2)`

To solve the radicals in the image, we can use the following properties of exponents:

`\sqrt[n]{a^(m) }` =
`a^{(m)/(n) }`

`a^(b)` .
`a^(c)` =
`a^(b+c)`

For the first radical, we can use the first property to simplify it as follows:

`\sqrt[3]{2 \cdot \sqrt[3]{2 \cdot \sqrt[4]{2}}}`=
`\sqrt[3]{2^2 \cdot 2^(1/4)}` =
`\sqrt[3]{2^3}` =
`\boxed{2}`

For the second radical, we can use the second property to simplify it as follows:

`\sqrt[4]{3^(17) + 9^(6)}` = +
`(3^2)^6}` =
`√(4) 3^(17)` + 3^{12}} =
`√(4){3^(17)`
`\cdot`
`(1 + 3^(5))}`

We can then use the first property to simplify the square root as follows:

`\sqrt{43^(17) }` .
`(1 + 3^(5))}` =
`\sqrt{43^(17) }` . 243} =
`√(4) 3^(17)` .
`3^5` =
`\sqrt[4]{3^(22)}` =
`\boxed{3^(11/2)}`

Therefore, the simplified expressions are:

`\sqrt[3]{2 \cdot \sqrt[3]{2 \cdot \sqrt[4]{2}}}` = 2

`\sqrt[4]{3^(17) + 9^(6)}` =
`3^(11/2)`