Learn how to evaluate a number raised to a rational exponent

The video tutorial explains the concept of exponents, specifically x to the m over n as the nth root of x to the m. It addresses the challenges of calculating large numbers like 81 cubed and suggests alternative methods for simplification. The importance of knowing common square and cube numbers is highlighted. The tutorial also covers the multiplication of exponents and provides tips for simplifying expressions. The session concludes with advice on simplifying calculations without extensive work.

What is the equivalent expression for x to the m over n?

• nth root of x to the m power

• mth root of x to the n power

• x to the n over m

• x to the m times n

Why might it be challenging to calculate 81 cubed without a calculator?

• It involves a large number of calculations.

• It requires knowledge of logarithms.

• It is impossible without a calculator.

• It needs advanced algebra skills.

What is a useful strategy for simplifying calculations involving powers?

• Knowing common square and cube numbers

• Using a calculator for all calculations

• Memorizing all powers up to 100

• Avoiding calculations altogether

What should you do when a base is raised to an exponent and then raised to another exponent?

• Multiply the exponents

• Add the exponents

• Subtract the exponents

• Divide the exponents

What is the simplified result of 6 cubed raised to the 2/3 power?

• 6

• 216

• 12

• 36