Understanding Exponent Properties

The video tutorial explains how to solve an equation by simplifying a rational expression using exponent properties. It begins with an introduction to the problem and encourages viewers to attempt solving it independently. The instructor then demonstrates the simplification process, explaining the properties of exponents in detail. Finally, the solution is derived by equating the simplified expression to find the value of K.

What assumption is made about the variable m in the problem?

• m is equal to zero

• m is a negative integer

• m is greater than zero

• m is less than zero

Which property of exponents is used to simplify the expression m^7/9 divided by m^1/3?

• Zero exponent

• Quotient of powers

• Power of a power

• Product of powers

What is the key realization when simplifying x^a / x^b?

• x^(a/b)

• x^(a+b)

• x^(a*b)

• x^(a-b)

What is the result of subtracting the exponents 7/9 and 1/3?

• 5/9

• 2/3

• 4/9

• 1/9

How is 1/3 expressed with a common denominator of 9?

• 3/9

• 1/9

• 4/9

• 2/9

What is the simplified form of m^(7/9) / m^(1/3)?

• m^(4/9)

• m^(5/9)

• m^(1/9)

• m^(2/3)

What is the equivalent expression for x^a times 1/x^b?

• x^(a+b)

• x^(a-b)

• x^(a*b)

• x^(a/b)

What is the common denominator used to subtract 7/9 and 1/3?

• 3

• 6

• 9

• 12

What is the value of K when m^(4/9) is equal to m^(K/9)?

• 5

• 4

• 3

• 2

What is the final step to find the value of K?

• Add the exponents

• Multiply the exponents

• Divide the exponents

• Equate the exponents