Rewriting a exponential equation to solve using one to one properties (2/3)^x = 4/9

The video tutorial explains the properties of exponents, focusing on how to handle expressions where an exponent is raised to another exponent. It uses a common example to demonstrate that when bases are the same, exponents can be set equal to solve for unknowns. The tutorial emphasizes rewriting expressions to have the same base, allowing for easier problem-solving. The session concludes with a promise of more examples to reinforce the concepts.

What is the result when an exponent is raised to another exponent?

• The exponents are added

• The exponents are multiplied

• The exponents remain unchanged

• The exponents are subtracted

If 2 raised to the power of 3x equals 2 raised to the power of 5, what is the value of x?

• 1

• 5

• 3

• 2

How can you solve an equation with different bases?

• By ignoring the bases

• By adding the bases

• By rewriting them to have the same base

• By subtracting the bases

What is the equivalent expression for 2/3 raised to the power of x when it equals 4/9?

• 2/3 raised to the power of 2

• 2/3 raised to the power of 1

• 2/3 raised to the power of 4

• 2/3 raised to the power of 3

Why is it important to rewrite bases in exponent problems?

• To make the problem more complex

• To simplify the problem

• To avoid solving the problem

• To change the base value