Question

How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents

Answer 1

Answer:

Radicals can be expressed as rational exponents and viceversa, that is,

$a^{\frac{n}{m}} = \sqrt[m]{a^n}$

That allows you to simplify expressions. Let's say, for example, you have:

$\sqrt[6]{4^3}$

Replacing 4 with 2^2 we get:

$\sqrt[6]{(2^2)^3}$

$\sqrt[6]{2^{2 \cdot 3}}$

Rewriting the radical as fractional exponent:

$2^{\frac{2 \cdot 3}{6}} = 2$

Answer 2

The properties of rational exponents can be applied to simplify expressions with radicals or rational exponents by writing radicals as numbers with rational exponents.

That allows you to apply the same properties of rational exponents to them.