Question

If the expression is written in rational exponent notation, rewrite notation, rewrite it in radical notation. If the the expression is written in radical notation, rewrite it in rational exponent notation.

Answer 1

To rewrite an expression in rational exponent notation, convert it to a base raised to a fractional exponent. To rewrite an expression in radical notation, express it as a root.

Step-by-step explanation:

To rewrite an expression in rational exponent notation, we need to convert it to a base raised to a fractional exponent. For example, if we have √a, we can rewrite it as a^(1/2). Similarly, to rewrite an expression in radical notation, we need to express it as a root. For instance, a^(3/4) can be written as the fourth root of a cubed, ∛a^3.

Let's consider an example: if we have (9^2/3), we can rewrite it as the cube root of 9 squared, ∛9^2. Similarly, if we have the square root of 16, we can rewrite it as 16^(1/2).

Answer 2

The expressions can be rewritten using the rule of exponent:

`x^{(a)/(b)}=\sqrt[b]{x^a}`

QUESTION A

`\sqrt[3]{12}`

In rational exponent form, we have the expression to be:

`\Rightarrow12^{(1)/(3)}`

QUESTION B

`\sqrt[4]{10^7}`

In rational exponent form, the expression will be:

`\Rightarrow10^{(7)/(4)}`

QUESTION C

`14^{(2)/(5)}`

In radical form, the expression will be:

`\Rightarrow\sqrt[5]{14^2}`

QUESTION D

`\sqrt[8]{15^3}`

In rational exponent form, the expression will be:

`\Rightarrow15^{(3)/(8)}`

QUESTION E

`21^{(9)/(4)}`

In radical form, the expression will be:

`\Rightarrow\sqrt[4]{21^9}`