Simplifying Expressions with Negative Rational Exponents

The video tutorial explains how to simplify expressions with negative rational exponents over real numbers. It covers two examples: simplifying negative eight raised to the power of negative four-thirds and negative 81 raised to the power of negative three-fourths. The first example is simplified to 1/16 using exponent rules and radical form. The second example is shown to have no real solution, as no real number raised to the fourth power equals negative 81. The tutorial emphasizes understanding the conversion between rational exponents and radical expressions.

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

• Multiply the base by the exponent

• Subtract the exponent from the base

• Convert the negative exponent to a positive by moving it to the denominator

• Add the exponent to the base

How do you rewrite a negative exponent as a positive exponent?

• By subtracting 1 from the exponent

• By multiplying the base by 2

• By adding 1 to the exponent

• By moving the base to the denominator

What does the denominator of a rational exponent indicate in radical form?

• The base of the expression

• The index of the root

• The exponent of the base

• The coefficient of the expression

What is the cube root of negative eight?

• Positive four

• Positive two

• Negative two

• Negative four

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

• Positive sixteen

• Positive eight

• Negative eight

• Negative sixteen

In the second example, what is the first step to simplify negative 81 raised to the power of negative three-fourths?

• Add the exponent to the base

• Subtract the exponent from the base

• Multiply the base by the exponent

• Convert the negative exponent to a positive by moving it to the denominator

What does the numerator of a rational exponent indicate in radical form?

• The index of the root

• The base of the expression

• The exponent of the base

• The coefficient of the expression

Why is the fourth root of negative 81 not real?

• Because negative 81 is not a perfect square

• Because there is no real number that can be raised to the fourth power to equal negative 81

• Because negative 81 is a complex number

• Because the base is negative

What should be entered in the homework system for an expression that is not real?

• D and E

• Not Real

• DNE

• NR

What is the final conclusion for the expression involving negative 81 raised to the power of negative three-fourths?

• The expression simplifies to a real number

• The expression is not real over the real numbers

• The expression is undefined

• The expression simplifies to zero