Factorization and Exponential Functions

The video tutorial explains how to solve an equation involving powers. It starts by setting up the problem and applying power rules to simplify the equation. The instructor then uses substitution to transform the equation into a quadratic form, which is factorized to find potential solutions. The video concludes by verifying the solution and confirming that x equals 2 is the correct answer.

What is the initial expression given in the problem?

• 4 to the power of x plus 4 to the power of x equals 272

• 4 to the power of x plus 4 to the power of 4 equals 272

• 4 to the power of x plus 4 to the power of 2 equals 272

• 4 to the power of x plus 4 to the power of 3 equals 272

What is the purpose of rewriting 4 to the power of 2 in the expression?

• To eliminate the variable

• To change the base of the power

• To simplify the equation

• To make the equation more complex

What mathematical rule allows us to swap the order of powers?

• Power Rule

• Division Rule

• Addition Rule

• Subtraction Rule

What substitution is made to simplify the equation?

• Let u equal 4 to the power of 4

• Let u equal 4 to the power of 3

• Let u equal 4 to the power of x

• Let u equal 4 to the power of 2

What is the quadratic equation formed after substitution?

• u squared minus u minus 272 equals zero

• u squared minus u plus 272 equals zero

• u squared plus u minus 272 equals zero

• u squared plus u plus 272 equals zero

What is the result of 16 squared?

• 289

• 256

• 225

• 272

What is the result of 17 squared?

• 225

• 256

• 289

• 272

Which two numbers multiply to 272 and have a difference of one?

• 18 and 19

• 17 and 18

• 16 and 17

• 15 and 16

What are the possible values of u after factorization?

• u equals 15 or u equals 16

• u equals 16 or u equals 17

• u equals 17 or u equals 18

• u equals 18 or u equals 19

What is the sum of 170 and 102?

• 272

• 256

• 289

• 225