Negative and Fractional Powers Explained

The video tutorial covers fractional powers, starting with an introduction to negative powers and their representation as fractions. It explains the concept of fractional powers involving roots and provides a general rule for calculating them. The tutorial also addresses fractional powers with numerators greater than one and negative fractional powers, offering examples and solutions to complex problems. The key takeaway is understanding how to apply the laws of indices to solve problems involving fractional and negative powers.

What is the result of 4 raised to the power of 1/2?

• 16

• 8

• 4

• 2

If a number is raised to the power of 1/3, what operation does this represent?

• Fifth root

• Fourth root

• Cube root

• Square root

How can 8 to the power of 4/3 be simplified?

• Cube root of 8, then raise to the power of 4

• Square root of 8, then raise to the power of 4

• Cube root of 8, then raise to the power of 3

• Fourth root of 8, then raise to the power of 3

What is the first step in simplifying 25 to the power of -3/2?

• Multiply by 2

• Take the reciprocal

• Add 3

• Subtract 2

What is the result of simplifying 36/16 to the power of -3/2?

• 8/27

• 27/8

• 64/216

• 216/64

How do you simplify 1/4 to the power of -2?

• Multiply by 2

• Take the reciprocal and square

• Add 4

• Subtract 2

What is the result of 64 to the power of -1/3?

• 1/8

• 8

• 1/4

• 4