Exponents and Their Properties

The video tutorial explains how to solve an exponential equation using exponent properties. It begins by rewriting the equation 2^2x as 2^2^x and simplifying it. The tutorial then demonstrates solving for x by combining like terms and dividing both sides of the equation. Next, it shows how to find a common base by expressing 64 as a power of 4. Finally, the solution is verified by substituting the value of x back into the original equation to ensure correctness.

What property of exponents is used to rewrite 2^(2x) in a simpler form?

• a^m * a^n = a^(m+n)

• a^m / a^n = a^(m-n)

• (a^m)^n = a^(m*n)

• a^0 = 1

After rewriting the equation, what is the next step in simplifying it?

• Add like terms on the left side

• Multiply both sides by 2

• Divide both sides by 4

• Subtract 4 from both sides

What is the result of dividing both sides of the equation by 2?

• 2x = 32

• 4x = 32

• 4x = 64

• 2x = 64

How can 64 be expressed as a power of 4?

• 4^4

• 4^2

• 4^3

• 4^5

What is the solution to the equation after equating the exponents?

• x = 5

• x = 3

• x = 2

• x = 4