Simplifying Expressions with Negative Rational Exponents

This video tutorial explains how to simplify expressions with negative rational exponents. It covers two examples: simplifying negative 64 raised to the power of -1/3 and negative 16 raised to the power of -1/2. The tutorial demonstrates using exponent rules to convert negative exponents to positive, rewriting expressions in radical form, and identifying perfect cube and square factors. It also discusses why certain expressions do not simplify over real numbers and briefly touches on complex numbers.

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

• Divide the base by the exponent

• Multiply the base by itself

• Convert the exponent to a positive exponent

• Add the exponent to the base

Which rule is used to convert a negative exponent to a positive exponent?

• Addition rule

• Exponent rule

• Subtraction rule

• Multiplication rule

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

• The base of the expression

• The coefficient of the expression

• The index of the radical

• The exponent of the base

How can negative 64 be expressed as a perfect cube?

• Negative 64 cannot be a perfect cube

• As negative four cubed

• As negative eight squared

• As negative two to the power of six

What is the simplified form of the cube root of negative 64?

• Negative 2

• Negative 16

• Negative 8

• Negative 4

What is the first step in simplifying negative 16 raised to the power of negative one-half?

• Convert the exponent to a positive exponent

• Multiply the base by itself

• Divide the base by the exponent

• Add the exponent to the base

What is the radical form of negative 16 raised to the power of one-half?

• Negative 16 to the power of two

• Fourth root of negative 16

• Square root of negative 16

• Cube root of negative 16

Why is negative 16 not a perfect square over real numbers?

• Because it is not divisible by 2

• Because no number times itself equals negative 16

• Because it is an even number

• Because it is a prime number

What should be entered in the homework system if the result is not real?

• NR

• N/A

• DNE

• INF

How can the square root of negative 16 be expressed using complex numbers?

• As 16i

• As 4i

• As 2i

• As 8i