Understanding Roots and Exponents

The video tutorial explains how to multiply roots with the same and different indices. It starts by demonstrating the multiplication of roots with the same index, where the exponents inside the roots are simply added. Then, it addresses the challenge of multiplying roots with different indices by converting them from radical to exponential notation, finding a common denominator, and adding the exponents. The tutorial concludes with an example involving the multiplication of square and cube roots, illustrating the process of converting to exponential notation, finding common denominators, and simplifying the expression.

What is the result of multiplying the fifth root of x cubed by the fifth root of x to the fourth?

• x to the sixth

• x to the fifth

• x to the seventh

• x squared

When multiplying expressions with different index numbers, what is the first step to simplify the expression?

• Add the exponents

• Convert to exponential notation

• Find a common base

• Multiply the bases directly

How do you add exponents with different denominators?

• Subtract the exponents

• Divide the exponents

• Find a common denominator

• Multiply the exponents

What is the equivalent of 5/3 in terms of a common denominator of 12?

• 10/12

• 20/12

• 25/12

• 15/12

What is the simplified form of the 12th root of x to the 29?

• x cubed times the 12th root of x to the fourth

• x to the fifth times the 12th root of x

• x squared times the 12th root of x to the fifth

• x to the fourth times the 12th root of x squared

In the example of multiplying the square root of x to the seven and the cube root of x to the fifth, what is the first step?

• Convert to radical form

• Add the exponents

• Convert to exponential notation

• Multiply the bases

What is the equivalent of 7/2 in terms of a common denominator of 6?

• 35/6

• 21/6

• 14/6

• 28/6

What is the final simplified form of the expression involving the square root of x to the seven and the cube root of x to the fifth?

• x to the fourth times the sixth root of x

• x to the seventh times the sixth root of x

• x to the fifth times the sixth root of x

• x to the sixth times the sixth root of x

What is the result of adding 21/6 and 10/6?

• 31/6

• 33/6

• 30/6

• 32/6

What is the sixth root of x to the 30 divided by 6?

• x to the seventh

• x to the sixth

• x to the fifth

• x to the fourth