Simplifying Expressions with Negative Rational Exponents

The video tutorial explains how to simplify expressions with negative rational exponents by converting them to positive exponents and using radical forms. It provides three examples: simplifying 9^(-3/2), (-8)^(-4/3), and (-81)^(-3/4). The first two examples are simplified and verified using a TI-84 calculator, while the third example demonstrates a non-real result. The tutorial emphasizes understanding the conversion process and the use of calculators for verification.

What is the first step in simplifying an expression with a negative rational exponent?

• Use the negative exponent property to rewrite it with a positive exponent.

• Add one to the exponent.

• Convert the expression to a decimal.

• Multiply the expression by zero.

When converting a rational exponent to radical form, what does the denominator indicate?

• The index of the radical.

• The exponent of the expression.

• The base of the expression.

• The coefficient of the expression.

What is the simplified form of 9 raised to the power of negative three halves?

• 1/27

• 1/9

• 1/3

• 27

Why is it necessary to keep negative bases in parentheses when raising them to a power?

• To ensure the base is positive.

• To avoid confusion with multiplication.

• To simplify the expression.

• To correctly apply the exponent to the entire base.

What is the simplified form of negative eight raised to the power of negative four thirds?

• 1/8

• 1/16

• 1/4

• 16

What is the result of raising negative two to the fourth power?

• -8

• 16

• 8

• -16

Why can't the fourth root of negative 81 be simplified over the real numbers?

• Because negative 81 is not a perfect square.

• Because there is no real number that raised to the fourth power equals negative 81.

• Because the base is too large.

• Because the exponent is not an integer.

What does DNE stand for in the context of simplifying expressions?

• Derivative Not Evaluated

• Decimal Notation Error

• Does Not Exist

• Denominator Not Equal

Why is it important to be in real mode when using a TI-84 calculator for these expressions?

• To increase calculation speed.

• To avoid complex number solutions.

• To save battery life.

• To ensure the calculator does not overheat.

What is the purpose of verifying expressions on a calculator?

• To confirm the expression is simplified correctly.

• To check for syntax errors.

• To find alternative solutions.

• To practice using the calculator.