Solving Equations and Exponents

Professor Dave explains algebraic roots and fractional exponents, demonstrating how to solve equations using these concepts. He starts with simple equations involving square roots and progresses to more complex ones with fractional exponents, emphasizing the importance of understanding the order of operations and the rules for manipulating exponents.

What is the equivalent of the square root of X in terms of fractional exponents?

• X to the power of 2

• X to the power of 1/2

• X to the power of 3

• X to the power of 1/3

In the equation √(X + 9) = 5, what is the first step to isolate X?

• Add 9 to both sides

• Take the cube root of both sides

• Square both sides

• Subtract 9 from both sides

After squaring both sides of the equation √(X + 9) = 5, what is the resulting equation?

• X + 9 = 5

• X + 9 = 25

• X = 25

• X = 5

How can you simplify the expression (X + 2)^(3/2) = 8?

• Take the square root of both sides

• Square both sides

• Raise both sides to the power of 2/3

• Raise both sides to the power of 3/2

What is the value of 8^(2/3)?

• 16

• 8

• 4

• 2

In the equation X^2 + 5 = 41, what should you do after subtracting 5 from both sides?

• Add 5 to both sides

• Square both sides

• Multiply both sides by 2

• Take the square root of both sides

When solving X^2 = 36, what are the possible solutions for X?

• 0

• 6 only

• -6 only

• 6 and -6

In the equation 3√(X - 1) = √(X + 1), what is the first step to eliminate the roots?

• Add 1 to both sides

• Subtract 1 from both sides

• Take the cube root of both sides

• Square both sides

After squaring both sides of 3√(X - 1) = √(X + 1), what is the expression on the left side?

• X + 1

• 9(X - 1)

• 3X - 1

• X - 1

What is the simplified solution for X in the equation 9(X - 1) = X + 1?

• X = 4/5

• X = 5/4

• X = 2

• X = 1