Exponential Equations and Properties

The video tutorial explains how to solve exponential equations using properties of exponents. It covers the concept of rewriting equations with a common base to simplify and solve them without logarithms. Two examples are provided: one involves rewriting bases to solve for x, and the other deals with fractions and negative exponents. The tutorial emphasizes the importance of having the same base to equate exponents and solve the equations.

What is the key property of exponents used to solve exponential equations with the same base?

• The bases are subtracted.

• The exponents are multiplied.

• The exponents are added.

• The exponents are equal.

In the first example, what is the common base used to solve the equation?

• Six

• Two

• Nine

• Three

What is the solution for 'x' in the first example after solving the equation?

• x = 14

• x = 7

• x = 4/19

• x = 19/4

In the second example, how is the number 64 expressed as a power of two?

• 2^5

• 2^4

• 2^7

• 2^6

What is the common base used in the second example to solve the equation?

• Six

• Eight

• Two

• Four

How is the fraction '1 over 2 squared' rewritten to have a common base in the second example?

• 2^-3

• 2^2

• 2^3

• 2^-2

What is the solution for 'x' in the second example after solving the equation?

• x = 4

• x = -2

• x = -4

• x = 2

What operation is performed when a power is raised to another power?

• Subtraction

• Addition

• Division

• Multiplication

What happens to the exponent when a term is moved across a fraction bar?

• It remains the same.

• It is doubled.

• It is halved.

• It changes sign.

What is the first step in solving an exponential equation with different bases?

• Divide the exponents.

• Find a common base.

• Add the exponents.

• Subtract the bases.