Solving Exponential Equations with Like Bases

The video tutorial explains how to solve exponential equations using the properties of exponents. It provides examples of solving equations with different bases, such as two and three, and demonstrates the use of prime factorization to simplify the process. The tutorial also covers how to handle negative exponents and concludes with a mention of additional examples available for further learning.

What is the value of x when 2 raised to the power of x equals 64?

• 4

• 6

• 2

• 8

How many factors of 2 are there in the number 64?

• 7

• 4

• 8

• 6

What is the equivalent expression for 64 in terms of powers of 2?

• 2 to the power of 7

• 2 to the power of 8

• 2 to the power of 6

• 2 to the power of 4

If the bases are the same and the equations are equal, what can be said about the exponents?

• They must be even

• They must be equal

• They must be opposites

• They must be prime numbers

What is the prime factorization of 64?

• 2 x 2 x 2 x 2 x 2 x 3

• 2 x 2 x 2 x 2 x 8

• 2 x 2 x 2 x 2 x 2 x 4

• 2 x 2 x 2 x 2 x 2 x 2

What is the value of x when 3 raised to the power of x equals 1/3 to the power of 4?

• 3

• -3

• 4

• -4

How can 81 be expressed as a power of 3?

• 3 to the power of 4

• 3 to the power of 6

• 3 to the power of 3

• 3 to the power of 5

What happens to the exponent when a fraction is moved from the denominator to the numerator?

• The exponent is squared

• The exponent is halved

• The exponent becomes positive

• The exponent becomes negative

What is the result of 3 to the power of -4?

• 1/16

• 1/64

• 1/81

• 1/49

What is the prime factorization of 81?

• 3 x 3 x 3 x 3 x 3

• 3 x 3 x 9

• 3 x 3 x 3 x 9

• 3 x 3 x 3 x 3