Simplifying Expressions with Rational Exponents

This video tutorial explains how to simplify expressions with both rational and integer exponents. It covers the order of operations, handling negative exponents by converting them to positive, and combining like terms. The tutorial concludes with a final simplification of the expression, ensuring no negative exponents remain.

What are rational exponents?

• Decimals

• Negative numbers

• Whole numbers

• Fractions

What is the first step in the order of operations for simplifying expressions?

• Handling exponents

• Combining like terms

• Simplifying fractions

• Dealing with parentheses

What does the power rule for exponents state?

• Divide the exponents

• Multiply the exponents

• Subtract the exponents

• Add the exponents

How do you handle negative exponents in a simplified expression?

• Subtract them from the positive exponents

• Add them to the positive exponents

• Convert them to positive exponents by taking the reciprocal

• Ignore them

What happens to a term with a negative exponent in the numerator when simplified?

• It stays in the numerator

• It is moved to the denominator

• It is removed from the expression

• It becomes zero

When combining like terms with the same base, what operation is performed on the exponents?

• Addition

• Subtraction

• Multiplication

• Division

What is the common denominator used for when adding fractions with different denominators?

• To simplify the fractions

• To make the denominators the same

• To multiply the fractions

• To divide the fractions

What is the quotient rule for exponents?

• Subtract the exponents

• Divide the exponents

• Multiply the exponents

• Add the exponents

What should be done if a negative exponent appears in the final simplified answer?

• Add it to the positive exponents

• Convert it to a positive exponent by taking the reciprocal

• Subtract it from the positive exponents

• Leave it as is

What is the final simplified form of the expression given in the video?

• 9 times y to the 1/6, over x to the 2/3

• 9 times y to the 2/3, over x to the 1/6

• 9 times x to the 2/3, over y to the 1/6

• 9 times x to the 1/6, over y to the 2/3