Learn to evaluate an expression with a negative rational power in denominator

The video tutorial explains how to evaluate expressions with rational exponents, focusing on converting negative exponents to positive ones. It demonstrates the process using the example of 81 raised to the 3/4 power, showing how to simplify the expression by rewriting 81 as a power of 3. The tutorial concludes with the final result of the evaluation.

What is the rule for converting a negative exponent to a positive one?

• Multiply the base by the exponent

• Take the reciprocal of the base and change the sign of the exponent

• Add the exponent to the base

• Divide the base by the exponent

How can 81 be rewritten as a power of a base to simplify the expression 81^(3/4)?

• 9^2

• 27^3

• 81^1

• 3^4

What is the result of raising 9^2 to the power of 3/4?

• 9^(6/4)

• 9^(3/2)

• 9^(5/4)

• 9^(1/2)

Why is it beneficial to rewrite 81 as 3^4 when simplifying the expression 81^(3/4)?

• It allows for easier cancellation of the denominator

• It reduces the exponent to zero

• It changes the base to a prime number

• It makes the base larger

What is the final result of evaluating 81^(3/4) using the alternative method?

• 27

• 81

• 9

• 3