Understanding Exponent Properties

The video tutorial explains how to solve an equation involving exponents. The goal is to find the value of K in the equation V^(-65) * fifth root of V = V^K, where V is greater than or equal to zero. The instructor guides the viewer through the process of using exponent properties to rewrite the equation consistently and solve for K. By applying the rule that allows the addition of exponents when multiplying like bases, the instructor demonstrates that K equals 1.

What is the initial equation given in the problem?

• V to the -65 power times the fifth root of V equals V to the K

• V to the 65 power times the fifth root of V equals V to the K

• V to the -65 power plus the fifth root of V equals V to the K

• V to the 65 power plus the fifth root of V equals V to the K

What is the fifth root of V expressed as an exponent?

• V to the 65 power

• V to the 1/65 power

• V to the 5 power

• V to the 1/5 power

Which property of exponents is used to combine V to the -65 and V to the 1/5?

• Division of exponents

• Subtraction of exponents

• Addition of exponents

• Multiplication of exponents

What is the result of combining the exponents -65 and 1/5?

• -64 4/5

• -65 1/5

• -64 1/5

• -65 4/5

What is the final value of K in the equation?

• 5

• 1

• -1

• 0