Exponential Equations and Properties

This video tutorial explains how to solve exponential equations by finding a common base on both sides of the equation. It demonstrates the process using two examples: 27^(3x+5) = 81^(4x+1) and 1/9^(2x) = 3^(7x-1). The tutorial covers factoring numbers to express them with the same base, applying exponent properties, and solving for x. It also explains how negative exponents create fractions and how to handle them in equations.

What is the first step in solving exponential expressions by finding the same base?

• Add the exponents on both sides.

• Multiply the numbers directly.

• Subtract the exponents on both sides.

• Factor the numbers to find a common base.

How can 27 be expressed as a power of 3?

• 3 to the power of 2

• 3 to the power of 3

• 3 to the power of 5

• 3 to the power of 4

What is the exponent property used when multiplying exponents inside parentheses?

• Divide the exponents

• Multiply the exponents

• Subtract the exponents

• Add the exponents

After finding the same base, what should be done with the exponents?

• Ignore them

• Add them together

• Set them equal to each other

• Subtract them

What is the solution for x in the equation 27^(3x+5) = 81^(4x+1)?

• x = 11/7

• x = 7/11

• x = 5/4

• x = 4/5

What type of exponent creates a fraction?

• Positive exponent

• Zero exponent

• Negative exponent

• Fractional exponent

How is 1/9 expressed as a power of 3 with a negative exponent?

• 3 to the power of -1

• 3 to the power of -2

• 3 to the power of -3

• 3 to the power of -4

What is the solution for x in the equation 1/9^(2x) = 3^(7x-1)?

• x = 1/11

• x = 7/1

• x = 11/1

• x = 1/7

What is the relationship between the exponents when the bases are the same?

• They are added together

• They are subtracted

• They are multiplied

• They are equal

What is the base of 9 when expressed as a power of 3?

• 3 to the power of 1

• 3 to the power of 2

• 3 to the power of 3

• 3 to the power of 4