Exponentiation and Linear Functions

The video tutorial explains how to solve the equation 4 to the 2X equals 1.44 and find the value of 4 to the X plus 1. It demonstrates the properties of exponentiation, showing how it transforms addition into multiplication. By rewriting 4 to the 2X as 4 to the X times 4 to the X, the tutorial finds that 4 to the X equals 1.2. This value is then used to calculate 4 to the X plus 1, resulting in 4.8.

What is the initial equation given in the problem?

• 4 to the X equals 1.44

• 4 to the 2X equals 1.44

• 4 to the X plus 1 equals 1.44

• 4 to the X equals 2.88

What does exponentiation transform addition into?

• Division

• Subtraction

• Exponentiation

• Multiplication

How can 4 to the X plus 1 be expressed using powers?

• 4 to the X minus 4 to the 1

• 4 to the X divided by 4 to the 1

• 4 to the X times 4 to the 1

• 4 to the X plus 4 to the 1

What is the next step after expressing 4 to the X plus 1 as a product of powers?

• Find 4 to the X minus 1

• Find 4 to the X plus 2

• Find 4 to the 2X

• Find 4 to the X

How is 4 to the 2X rewritten to solve the equation?

• 4 to the X plus X

• 4 to the X minus X

• 4 to the X times X

• 4 to the X divided by X

What is the relationship between 4 to the X and 4 to the 2X?

• 4 to the X is half of 4 to the 2X

• 4 to the X is double 4 to the 2X

• 4 to the X is the square of 4 to the 2X

• 4 to the X is the square root of 4 to the 2X

What mathematical property allows us to express 4 to the 2X as 4 to the X times 4 to the X?

• Associative property

• Commutative property

• Distributive property

• Exponentiation property

What is 1.44 rewritten as to find 4 to the X?

• 1.2 minus 1.2

• 1.2 divided by 1.2

• 1.2 plus 1.2

• 1.2 times 1.2

What is the value of 4 to the X?

• 4.8

• 1.44

• 2.4

• 1.2

What is the purpose of rewriting 1.44 as 1.2 times 1.2?

• To simplify the equation

• To find the value of 4 to the 2X

• To find the value of 4 to the X

• To find the value of 4 to the X plus 1