Exploring Nth Roots and Rational Exponents

What does the denominator in a rational exponent indicate when converting to radical form?

• It indicates the type of operation to perform.

• It represents the root to be taken.

• It suggests the power to which the number is raised.

• It determines the number of terms in the expression.

If you have a square root of 18, which is broken down into 2 * 9, what is the simplified form?

• 2 + 3

• 3 + 3

• 3 * 3

• 2 * 3

What is the result of taking the square root of a negative number?

• A positive number

• A negative number

• Zero

• A complex number

How do you handle a negative exponent when it appears in a radical expression?

• Ignore the negative sign.

• Multiply by a negative one.

• Convert the expression to a fraction.

• Add it to the numerator.

When simplifying the expression 2 to the power of 6 under a cube root, what is the simplified form?

• 6 to the power of 2

• 3 to the power of 2

• 2 to the power of 3

• 2 to the power of 2

What does the fifth root of 100 simplify to, given the prime factorization?

• 2

• 5

• 10

• Cannot be simplified further

In the context of roots, what does an even root imply about the result?

• Always negative

• None of the above

• Always positive

• Can be positive or negative

How do you solve an equation involving a cube root to isolate the variable?

• Take the cube root of both sides

• None of the above

• Take the square root of both sides

• Multiply both sides by three

What is the result of simplifying the fourth root of 16?

• 2

• 16

• 4

• 8

If you have the expression (4x^5)^2/3, how is it properly simplified?

• Cannot be simplified

• 16x^15

• 8x^10

• 4^(2/3) x^(10/3)