Understanding Rational Exponents and Powers

This video tutorial reviews rational exponents, focusing on their properties and how to manipulate and simplify expressions using them. It begins with a review of basic exponent rules, including multiplication, division, power of a power, and negative exponents. The tutorial then explains rational exponents, how to convert them to radical form, and provides examples to illustrate these concepts. The video concludes with verification of examples and a summary of the key points discussed.

What should you do with the exponents when multiplying two powers with the same base?

• Divide the exponents

• Subtract the exponents

• Add the exponents

• Multiply the exponents

When dividing powers with the same base, what is the correct operation to perform on the exponents?

• Add the exponents

• Multiply the exponents

• Subtract the exponents

• Divide the exponents

How do you simplify a power raised to another power?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

What happens to the exponent when you have a negative exponent?

• It becomes positive

• It remains negative

• It is multiplied by -1

• It is divided by -1

In a rational exponent, what does the denominator represent?

• The coefficient of the term

• The base of the power

• The index of the radical

• The exponent of the power

How can you express the cube root of a number using rational exponents?

• As the number raised to the power of 1/3

• As the number raised to the power of 3/2

• As the number raised to the power of 2/3

• As the number raised to the power of 1/2

What is the rational exponent form of the square root of x?

• x to the power of 1/2

• x to the power of 2/3

• x to the power of 1/3

• x to the power of 3/2

If you have a base raised to a fractional power, what does the numerator of the exponent indicate?

• The coefficient of the term

• The index of the radical

• The base of the power

• The exponent of the radical

How do you simplify 8 raised to the power of 4/3?

• 8

• 16

• 2

• 4

What is the fourth root of 81 raised to the third power?

• 3

• 81

• 27

• 9