Exponential Functions and Equations

This lesson covers solving exponential equations with like bases. It begins with an introduction to the concept and proceeds with several examples, each increasing in complexity. The examples demonstrate solving equations using properties of exponents, negative exponents, factorization, power rules, and radical notation. The lesson emphasizes setting exponents equal when bases are the same and manipulating equations to achieve like bases.

What is the basic rule for solving exponential equations with like bases?

• Set the bases equal to each other.

• Set the exponents equal to each other.

• Multiply the exponents.

• Divide the bases.

In the equation 2^(5x - 7) = 64, what is the value of x?

• 7

• 6

• 5/13

• 13/5

How can 1/7 be expressed using exponents?

• 7^-1

• 7^1

• 7^2

• 7^0

What is the result of solving the equation 1/7^(6x) = 343?

• x = 1/2

• x = -1/2

• x = -3

• x = 3

What is the base used to simplify the equation 216^(-4x + 7) = 36^(2x + 1)?

• 9

• 6

• 2

• 3

In the equation 32^(5 - 3x) * 64^(-2x - 1) = 1/8, what is the common base used?

• 16

• 2

• 8

• 4

What is the simplified form of 1/8 using a negative exponent?

• 2^-3

• 2^3

• 8^-1

• 8^1

How can the expression x^(2/3) be rewritten using radical notation?

• Cube of square root of x

• Cube root of x squared

• Square of cube root of x

• Square root of x cubed

What are the solutions for x in the equation 4 = x^(2/3)?

• x = ±4

• x = ±8

• x = 8

• x = 4

What is the cube root of 8?

• 1

• 2

• 3

• 4