Exponential Equations and Factorization

The video tutorial explains how to solve exponential equations by using like bases. It demonstrates the process with two examples: one involving the equation 27^x = 2187 and another with (1/16)^x = 32. The tutorial emphasizes the importance of rewriting both sides of the equation with the same base, using prime factorization, and applying the rule that if the bases are the same, the exponents must be equal. The video also covers handling fractional bases and negative exponents.

What is the first step in solving exponential equations using like bases?

• Divide the exponents

• Multiply the bases

• Add the exponents

• Convert both sides to the same base

In the equation 27^x = 2187, why can't we use 27 as a base for 2187?

• 2187 is a prime number

• 27 is greater than 2187

• 27 is not a prime number

• 2187 is not a power of 27

What is the prime factorization of 27?

• 27 x 1

• 3 x 9

• 9 x 3

• 3 x 3 x 3

How many factors of 3 are there in 2187?

• 7

• 5

• 6

• 8

What is the process called when breaking down a number into its prime factors?

• Exponentiation

• Fraction simplification

• Prime factorization

• Base conversion

What is the value of x in the equation 3^(3x) = 3^7?

• 7/3

• 3

• 3/7

• 7

In the equation (1/16)^x = 32, what is the base used for both sides?

• 16

• 4

• 32

• 2

What is the equivalent expression for 1/16 in terms of base 2?

• 2^4

• 2^-4

• 2^2

• 2^-2

What is the value of x in the equation 2^(-4x) = 2^5?

• -4/5

• 5/4

• -5/4

• 4/5

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

• The exponent is halved

• The exponent is doubled

• The sign of the exponent changes

• The exponent remains the same