Exponential Equations and Properties

The video tutorial explains how to solve exponential equations by using like bases. It demonstrates that if two exponential expressions have the same base, their exponents must be equal. The tutorial provides two examples: one with base five and another with base three, showing step-by-step how to isolate the exponential part and equate the exponents. The video concludes with a brief mention of upcoming examples in the next video.

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

• Multiply both sides by the base

• Isolate the exponential part on one side

• Subtract the base from both sides

• Add the same number to both sides

If 'a' to the power of 'm' equals 'a' to the power of 'n', what can be concluded?

• m and n are unrelated

• m is greater than n

• m is equal to n

• m is less than n

In the first example, what operation is used to isolate 'five raised to the power of x'?

• Multiplication

• Division

• Addition

• Subtraction

What is 125 expressed as a power of five?

• Five to the third

• Five to the fifth

• Five to the fourth

• Five to the second

What is the value of x when 'five to the power of x' equals 'five to the third'?

• 4

• 3

• 2

• 1

In the second example, what is the first step to isolate 'three raised to the power of x'?

• Subtract 32 from both sides

• Divide both sides by 6

• Multiply both sides by 6

• Add 32 to both sides

What is 243 expressed as a power of three?

• Three to the third

• Three to the fourth

• Three to the fifth

• Three to the sixth

What is the value of x when 'three to the power of x' equals 'three to the fifth'?

• 3

• 4

• 5

• 6

How can you determine if a number is divisible by three?

• If the number ends in 5

• If the sum of its digits is divisible by three

• If the number is a multiple of 10

• If the number is even

What is the relationship between the exponents when two exponential expressions with the same base are equal?

• The exponents are unrelated

• The exponents are inverses

• The exponents are different

• The exponents are equal