Exponential Equations and Powers

The video tutorial explains how to solve exponential equations by using properties of exponents. It covers the method of equating exponents when both sides of an equation have the same base. The tutorial provides examples with different bases, including base 2, base 5, and base 3, demonstrating how to manipulate and solve these equations using exponent rules such as the product rule and power rule.

What is an exponential equation?

• An equation with a constant exponent

• An equation with no variables

• An equation with a variable in the exponent

• An equation with a variable in the base

In the equation 2^(3x + 5) = 16, where is the variable located?

• In the exponent

• In the base

• In the constant term

• In the coefficient

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

• If the exponents are different, the bases are equal

• If the bases are equal, the exponents are equal

• If the exponents are equal, the bases are equal

• If the bases are different, the exponents are equal

What must be true for the property 'if B^x = P^y, then x = y' to hold?

• P must not equal 1

• B must equal 1

• B must not equal 1

• P must equal 1

How can 16 be expressed as a power of 2?

• 2^5

• 2^4

• 2^3

• 2^2

What is the solution for x in the equation 2^(3x + 5) = 2^4?

• x = 3

• x = 4

• x = -1/3

• x = 1

How is the square root of 5 expressed as a power of 5?

• 5^1

• 5^2

• 5^(3/2)

• 5^(1/2)

What is the result of moving an expression from the denominator to the numerator?

• The exponent becomes positive

• The expression is squared

• The base changes

• The exponent becomes negative

What is the solution for x in the equation 5^(x + 2/3) = 5^(-1/2)?

• x = -1/2

• x = -1/3

• x = 1/2

• x = -7/2

How can 8 be expressed as a power of 2?

• 2^2

• 2^3

• 2^4

• 2^5