How to evaluate a number raised to a rational exponent

The video tutorial focuses on teaching students how to perform mathematical operations without using a calculator. It explains the process of rewriting the number 27 as a different base and applying the power rule to simplify expressions. The tutorial emphasizes understanding the concepts behind the calculations and concludes with an invitation for questions.

What is the main goal of the lesson as introduced by the teacher?

• To memorize mathematical formulas.

• To solve problems without using a calculator.

• To understand the history of mathematics.

• To learn how to use a calculator effectively.

How can the number 27 be expressed using a different base?

• As 4 to the power of 3.

• As 5 to the power of 3.

• As 3 to the power of 3.

• As 2 to the power of 3.

What is the first step in rewriting 27 raised to the 2/3 power?

• Divide 27 by 3.

• Convert 27 to base 2.

• Express 27 as 3 to the 1/3 power.

• Multiply 27 by 2/3.

What rule is applied to simplify the expression 3 to the 1/3 power times 2/3?

• The subtraction rule.

• The power rule.

• The addition rule.

• The division rule.

What is the final result of simplifying 27 raised to the 2/3 power?

• 6

• 15

• 9

• 12