Evaluating a number raised to a rational exponent

The video tutorial explains how to simplify and evaluate the expression 256 to the 3/8. It begins by introducing the problem and explores rewriting the expression in radical form. The tutorial then demonstrates how to simplify the expression using powers of 4 and evaluates it without a calculator. The session concludes with a summary and a preview of upcoming examples.

What is the radical form of 256 raised to the power of 3/8?

• The 3rd root of 256 to the 8th power

• The 8th root of 256 cubed

• The 8th root of 256 squared

• The 3rd root of 256 squared

How can 256 be expressed as a power of 4?

• 4 to the 5th power

• 4 to the 3rd power

• 4 to the 6th power

• 4 to the 4th power

What is the simplified form of 4 raised to the power of 12/8?

• 4 to the power of 2

• 4 to the power of 3/2

• 4 to the power of 2/3

• 4 to the power of 1/2

What is the value of the square root of 4 cubed?

• 32

• 8

• 16

• 64

Which method can be used to solve 256 to the power of 3/8 without a calculator?

• Using logarithms

• Applying calculus

• Simplifying exponents

• Using trigonometry