Understanding Roots and Exponents

The video tutorial explores the concept of equivalent expressions, focusing on the seventh root of v to the third power. It explains how to convert roots into fractional exponents and apply exponent properties to determine equivalency. The tutorial also covers solving equations involving roots and constants, emphasizing the use of reciprocal and negative exponents. Through examples, it demonstrates how to find the value of a constant in equations and clarifies the relationship between different forms of expressions.

What is a good method to determine if expressions are equivalent?

• Convert them to the same form

• Compare their coefficients

• Check their constants

• Evaluate them at zero

What is the seventh root of v to the third power equivalent to?

• v to the 1/7 power

• v to the 7/3 power

• v to the 3/7 power

• v to the 1/3 power

Which of the following is equivalent to v to the 3/7 power?

• v to the 3/7 power

• v to the 7/3 power

• v to the 1/7 power

• v to the 1/3 power

Is the cube root of v to the seventh power equivalent to v to the three-sevenths power?

• Yes, for all values of v

• No, it is equivalent to v to the one-third power

• No, it is equivalent to v to the seven-thirds power

• Yes, but only for positive values of v

What is the sixth root of g to the fifth power equivalent to?

• g to the 5/7 power

• g to the 6/5 power

• g to the 5/6 power

• g to the 1/6 power

What is the value of d if the sixth root of g to the fifth power is equal to g to the d?

• 1/6

• 5/6

• 6/5

• 5/7

What is the seventh root of x equivalent to?

• x to the 1/7 power

• x to the 7/1 power

• x to the 1/3 power

• x to the 3/7 power

What is the value of d if 1 over the seventh root of x is equal to x to the d?

• 1/7

• -1/7

• -7/1

• 7/1

What happens when you take the reciprocal of something raised to a power?

• It doubles the power

• It becomes the negative of that power

• It squares the power

• It halves the power

How can you rewrite 1 over the seventh root of x?

• x to the -7/1 power

• x to the 7/1 power

• x to the -1/7 power

• x to the 1/7 power