Nth root and rational exponents

Rational Exponents

Fractional Exponents. A rational exponent represents both an integer exponent and an nth root. 

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This is read as the 5th root of 18

Square Root

A square root of a number is a value that can be multiplied by itself to give the original number.

A square root of 49 is 7, because when 7 is multiplied by itself we get 49.

nth Roots

Simplify

Simplify

Simplify

Rational Exponents

• The numerator (top of the fraction) is the exponent

• Hint: exponent goes at the TOP of the number

• The denominator (bottom of the fraction) is the root

• Hint: the roots are at the BOTTOM of the tree.

Lets step it up a tiny bit

Multiple Choice

Write the expression in radical form.

x^7/2

• √x⁷

• 7√x²

• 7x²

• ∛x⁷

Multiple Choice

Write in exponential form

∛x⁷

• $$x^{\frac{7}{3}}$$

• $$x^{\frac{3}{7}}$$

• 3x⁷

• 7x³

Multiple Choice

Simplify.

• $$x^3y^9$$  

• $$x^2y^9$$  

• $$x^2y^4$$  

Multiple Choice

Write in exponential form:

$$\ ^5\sqrt{h}$$  

• $$h^{\frac{1}{5}}$$  

• $$h^{\frac{5}{1}}$$  

• $$h^{\frac{5}{2}}$$  

• $$h^{\frac{2}{5}}$$  

Multiple Choice

Write in exponential form: $$\ ^3\sqrt{y^5}$$  

• $$y^{\frac{5}{3}}$$  

• $$y^{\frac{3}{5}}$$  

Multiple Choice

Write in radical form:  $$17^{\frac{1}{3}}$$  

• $$\ ^3\sqrt{17^1}$$  

• $$\ ^1\sqrt{17^3}$$  

• $$\ ^2\sqrt{17^3}$$  

Multiple Choice

Write in radical form: 

$$m^{\frac{2}{3}}$$  

• $$\ ^3\sqrt{m^2}$$  

• $$\ ^2\sqrt{m^3}$$