Exponential Equations and Prime Factorization

The video tutorial explains how to solve exponential equations by making the bases the same, allowing for simplification. It covers breaking numbers down to their prime factors, using exponent rules, and demonstrates the prime factorization of 128. Additionally, it shows how to use a calculator for quick factorization. The tutorial emphasizes the beauty of mathematics in understanding these processes.

What is the main goal when solving exponential equations?

• To find the largest number

• To make the bases the same

• To divide the coefficients

• To multiply the exponents

Why can't the number 3 be broken down further?

• Because it is a prime number

• Because it is an even number

• Because it is a composite number

• Because it is a perfect square

What is the prime factorization of 128?

• 2^7

• 2^6

• 5^2

• 3^4

Which of the following is a correct breakdown of 128?

• 64 x 3

• 10 x 12

• 32 x 4

• 16 x 8

What are prime numbers often referred to as in mathematics?

• The smallest numbers

• The largest numbers

• The building blocks

• The end of calculations

Which of the following is NOT a method to break down 128?

• 64 x 2

• 32 x 4

• 16 x 8

• 50 x 2

What is the fast way to find the prime factorization of a number using a calculator?

• Use the addition function

• Use the subtraction function

• Use the division function

• Use the fact function

After making the bases the same, what is the next step in solving the equation?

• Multiply the coefficients

• Cancel the bases

• Add the exponents

• Divide the exponents

What is the value of x in the equation 2^2x = 2^7?

• x = 3.5

• x = 7

• x = 2

• x = 5

What is the result of dividing both sides of the equation 2x = 7 by 2?

• x = 3.5

• x = 7

• x = 2

• x = 5