Rational Exponents

Simplify: @@ ext{Root}(x^8)@@

• @@x^2@@

• @@x^3@@

• @@x^4@@

• @@x^5@@

What is the relationship between rational exponents and roots?

• Rational exponents can be expressed as roots, specifically, if @@a^{\frac{m}{n}}@@, it can be rewritten as @@\frac{m}{\text{Root}(n)}@@.

• Rational exponents are always integers and cannot be expressed as roots.

• Rational exponents are the same as whole number exponents and do not involve roots.

• Rational exponents can only be expressed as fractions, not as roots.

Simplify: @@\frac{27^{\frac{2}{3}}}{3^{\frac{4}{3}}}@@

• @@3^{\frac{2}{3}}@@

• @@3^{\frac{4}{3}}@@

• @@9@@

• @@27@@

Convert @@16^{\frac{3}{4}}@@ to radical form.

• @@\text{Root}(4)(16^3)@@

• @@\text{Root}(3)(16^4)@@

• @@\text{Root}(4)(16^{\frac{3}{2}})@@

• @@\text{Root}(2)(16^3)@@

• 0

• 1

• x

• undefined

Simplify: @@\frac{1}{4^{\frac{1}{2}}}@@

• @@\frac{1}{4}@@

• @@\frac{1}{3}@@

• @@\frac{1}{2}@@

• @@\frac{1}{1}@@

• It represents the conversion of a rational exponent to its equivalent radical form.

• It indicates the power of a number raised to a whole number.

• It shows the relationship between integers and fractions.

• It defines the process of simplifying radical expressions.

How do you simplify @@\frac{a^{\frac{m}{n}}}{b^{\frac{m}{n}}}@@?

• @@\frac{a}{b}^{\frac{m}{n}}@@

• @@\frac{a^{m}}{b^{n}}@@

• @@\frac{a^{m/n}}{b^{m/n}}@@

• @@\frac{a^{m+n}}{b^{m+n}}@@

What is the value of @@8^{\frac{1}{3}}@@?

• 1

• 2

• 3

• 4

What is the simplified form of @@\frac{1}{\text{Root}(x^2)}@@?

• @@\frac{1}{x}@@, for @@x > 0@@

• @@\frac{1}{x^2}@@, for @@x > 0@@

• @@\frac{1}{\sqrt{x}}@@, for @@x > 0@@

• @@\frac{1}{\text{Root}(x)}@@, for @@x > 0@@