Exponent Rules and Simplification

The video tutorial explains exponent rules, focusing on multiplying and dividing like bases. It covers how to add exponents when multiplying like bases and how to handle cube roots when exponents are the same. The tutorial also addresses dividing like bases by subtracting exponents and managing negative exponents, ensuring no rational exponents remain in the denominator.

What is the rule for exponents when multiplying like bases?

• Divide the exponents

• Subtract the exponents

• Add the exponents

• Multiply the exponents

How do you simplify 2^(1/4) * 2^(1/3)?

• 2^(3/4)

• 2^(1/7)

• 2^(7/12)

• 2^(1/12)

When exponents are the same, how can you simplify the expression 5^(1/3) * 2^(1/3)?

• 5^(1/3) + 2^(1/3)

• Cube root of 10

• 5^(1/3) * 2^(1/3)

• Cube root of 7

What is the simplified form of 8^(1/3)?

• 1

• 4

• 2

• 3

What operation is performed on exponents when dividing like bases?

• Subtract the exponents

• Divide the exponents

• Multiply the exponents

• Add the exponents

How do you handle a negative exponent in the denominator?

• Convert it to a positive exponent in the denominator

• Ignore the negative sign

• Convert it to a positive exponent in the numerator

• Leave it as is

What is the result of x^(1/4) - x^(1/12)?

• x^(1/3)

• x^(1/12)

• x^(1/6)

• x^(1/4)

Why can't you leave a root in the denominator?

• It is mathematically incorrect

• It is not simplified

• It is not allowed in final answers

• It is not a whole number

What is the purpose of multiplying the denominator by x^(3/4)?

• To eliminate the base

• To add more complexity

• To simplify the numerator

• To make the exponent a whole number

What is the final form of x^(3/4) over x^(1)?

• x^(1/4)

• x^(1/2)

• x^(3/4)

• x^(1)