How to evaluate a number raised to a negative rational exponent

The video tutorial explains how to solve the problem of 81 raised to the negative 3/4 power. It begins by introducing the problem and discussing the rules for handling negative exponents. The teacher explains the exponent rule x to the m over n equals the n-th root of x to the m power. The video then demonstrates how to apply this rule to the given problem, addressing the confusion around negative exponents. Finally, the teacher simplifies the expression and finds the solution, offering an alternative method for simplification.

What is the rule for converting a fractional exponent into a root and power?

• x to the m over n is equal to x to the n divided by m

• x to the m over n is equal to x to the m times n

• x to the m over n is equal to the n-th root of x to the m power

• x to the m over n is equal to the m-th root of x to the n power

How can you rewrite an expression with a negative exponent?

• Multiply the base by the negative exponent

• Add the negative exponent to the base

• Subtract the negative exponent from the base

• Rewrite it as 1 over the base raised to the positive exponent

What is the value of 81 raised to the 3rd power?

• 9,261

• 27,000

• 531,441

• 729

What is the simplified result of 81 to the 3/4 power?

• 1/27

• 1/81

• 1/9

• 1/3

What alternative method can be used to simplify the expression 81 to the 3/4 power?

• Using a simpler root calculation

• Using logarithms

• Using a calculator

• Using a different exponent rule