Exploring Properties of Rational Exponents and Radicals

This video tutorial covers properties of rational exponents and radicals, focusing on addition and subtraction of radicals, simplifying radicals with variables, rationalizing denominators, and applying rules of exponents. The instructor provides examples and explains the importance of matching radicals for addition and subtraction, simplifying radicals with variables, and rationalizing denominators. The video concludes with applying exponent rules in calculations.

What must be true for two radicals to be added or subtracted?

• Both A and B.

• They must have the same numerical value under the radical.

• They must be in simplest form.

• They must have the same index number.

If you have 5 times the third root of 7 plus 6 times the third root of 7, what is the result?

• Cannot be simplified

• 1 times the third root of 7

• 30 times the third root of 7

• 11 times the third root of 7

How do you simplify the third root of 27d^12?

• d^3

• d^4

• 3d^4

• 3d^3

What is the fourth root of x^4 divided by the fourth root of y^16?

• x^4/y^4

• x/y^4

• x^4/y

• x/y

How do you simplify the third root of 2a^13b^3c^8?

• a^4bc^2 times the third root of 2b

• a^4b^3c^2 times the third root of 2

• a^4bc^2 times the third root of 2ac^2

• a^4bc^2 times the third root of 2c

What is the simplified form of the fourth root of 486x^7y^10z^13?

• 3xy^2z^3 times the fourth root of 6x^3y^2z

• 3xy^2z^3 times the fourth root of 6x^3yz

• 3x^2y^2z^3 times the fourth root of 6xy^2z

• 3xy^2z^3 times the fourth root of 6x^3y^2z^2

How do you rationalize the denominator of x^2 divided by the third root of y^13?

• Multiply by the third root of y^3

• Multiply by the third root of y^2

• Multiply by the third root of y^4

• Multiply by the third root of y

What is the simplified form of 16x divided by 8x^(2/3)?

• 2x^(1/3)

• 2x^(2/3)

• 2x

• 2x^(4/3)

How do you combine 6 times the third root of x plus 2 times the third root of x?

• 8 times the third root of x

• 4 times the third root of x

• 6 times the third root of x

• Cannot be combined

What is the simplified form of 16p times the fourth root of 3p^2 minus 2p times the fourth root of 3p^2?

• 14p times the fourth root of 3p^2

• 14p times the fourth root of 3p

• 14p times the fourth root of 3

• 14p times the fourth root of p^2