Rational Exponents: Converting Between Forms

This video tutorial introduces the concept of rational exponents, explaining that they are exponents in fraction form. It covers the difference between radical and exponential forms and provides methods for converting between the two. The tutorial includes examples and practice problems to reinforce understanding, with a focus on the power-over-root rule for conversions.

What does 'rational' in rational exponents refer to?

• Whole numbers

• Fractional form

• Irrational numbers

• Exponential form

How is a radical expression written in exponential form?

• Root over power

• Base over power

• Power over root

• Power over base

What is the exponential form of the third root of x squared?

• x cubed

• x squared

• x to the power 3/2

• x to the power 2/3

If an expression is in radical form with a root index of 2, how would it appear in exponential form?

• Base to the power 2

• Power over 2

• 2 over power

• Base to the power 1/2

How do you convert x to the 2/3 power back to radical form?

• Cube root of x squared

• Square root of x cubed

• x to the power 2/3

• x to the power 3/2

What does the expression x^3 y^5 z^1/2 represent in radical form?

• Cube root of x cubed, y to the fifth, z

• Square root of x cubed, y to the fifth, z

• Cube root of x, y, z to the half

• Square root of x, y cubed, z

In the expression x^1 y^3 under a single radical with a root of 2, how is it simplified?

• Cube root of x times y

• Square root of x times y cubed

• Cube root of x plus y cubed

• Square root of x plus y cubed

What is the radical form of a^2 b^3 c^4 all raised to the 1/3 power?

• Cube root of a squared, b cubed, c to the fourth

• Square root of a, b, c

• Cube root of a, b, c

• Square root of a squared, b cubed, c to the fourth

How is the cube root of all variables raised to the first power expressed in exponential form?

• Variables to the power 1/2

• Variables to the power 1

• Variables to the power 3

• Variables to the power 1/3

What is the correct exponential form for the square root of x y cubed?

• x y^3/2

• x^1/2 y^3

• x^1 y^3

• x^1/2 y^3/2