Simplifying Exponents and Roots

The video tutorial guides viewers through the process of simplifying the expression 9p to the 2/3 over the square root of 4p cubed. It breaks down the expression into manageable parts, simplifies the numerator and denominator separately, and uses negative exponents to further simplify the expression. The tutorial concludes with the final simplified form of the expression, providing a clear understanding of the mathematical operations involved.

What is the first step in simplifying the expression 9p^(2/3) over the square root of 4p^3?

• Add the exponents of p

• Break down the numerator and denominator separately

• Convert the entire expression to a single fraction

• Multiply the numerator by the denominator

How can the square root of 4p^3 be expressed in terms of exponents?

• 4p^3 to the power of 3/2

• 4p^3 to the power of 1/2

• 4p^3 to the power of 2

• 4p^3 to the power of 1/3

What is the principal root of 4?

• 4

• 1

• 2

• 3

How can 9^(2/3) be expressed for simplification?

• 9 cubed to the power of 1/3

• 9 to the power of 1/2

• 9 squared to the power of 1/3

• 9 to the power of 3

What is the simplified form of p^3 to the power of 1/2?

• p^(3/2)

• p^(1/3)

• p^(2/3)

• p^(1/2)

How is 81 factored to simplify 81^(1/3)?

• 3 times 3 times 3

• 3 times 9

• 3 to the power of 4

• 3 to the power of 3

What is the result of subtracting the exponents 2/3 and 3/2?

• 5/6

• -5/6

• -1/6

• 1/6

What is the cube root of 27?

• 4

• 2

• 1

• 3

In the final expression, how is p to the negative 5/6 represented?

• As a positive exponent

• As a fraction

• As a decimal

• As a negative exponent

What is the final simplified form of the expression?

• 1.5 times p^(-5/6) times the cube root of 3

• 3/2 times p^(5/6) times the cube root of 3

• 3/2 times p^(-5/6) times the cube root of 3

• 1.5 times p^(5/6) times the cube root of 3