Equating Exponents and Simplifying Powers

The video tutorial explains how to solve a nested exponential equation by manipulating and simplifying the equation. It begins with an introduction to the problem, followed by rewriting the equation to isolate terms. The tutorial then focuses on simplifying exponents using power rules and equating exponents to solve for the variable x. The final solution is derived, concluding with the value of x. The video encourages viewers to subscribe for more content.

What is the main objective of the video tutorial?

• To explore geometry problems

• To solve a nested exponential equation

• To learn about basic algebra

• To understand calculus concepts

What is the first step taken to solve the equation?

• Add 3^2 to both sides

• Move 2^162 to the other side

• Divide both sides by 2

• Multiply both sides by x

What is the rewritten form of the equation after moving 2^162?

• 4^(2^3)^x = 3^162

• 4^(3^2)^x = 2^162

• 3^(4^2)^x = 2^162

• 2^(3^2)^x = 4^162

How is the exponent 162 simplified?

• As 5 times 32.4

• As 2 times 81

• As 3 times 54

• As 4 times 40.5

What rule is applied to simplify the expression 2^162?

• Division rule of exponents

• Power rule of exponents

• Subtraction rule of exponents

• Addition rule of exponents

What is the simplified form of 2^162?

• 8^54

• 16^40.5

• 32^32.4

• 4^81

What is the next step after rewriting 2^162 as 4^81?

• Equate the exponents

• Multiply both sides by 3

• Subtract 2 from both sides

• Add 4 to both sides

What allows us to equate the exponents in the equation?

• The variables are the same

• The bases are the same

• The coefficients are equal

• The terms are identical

How is 81 expressed in terms of powers of 3?

• 3^6

• 3^5

• 3^3

• 3^4

What is the equation after equating the exponents of 3?

• 3^x = 4

• 2^x = 4

• 5^x = 3

• 4^x = 2