Q1. Simplify the exponential expression:

Background

Topic: Properties of Exponents

This question tests your ability to apply the rules of exponents, including multiplying powers with the same base and handling negative exponents.

Key Terms and Formulas

• Product of Powers:

• Negative Exponent:

Step-by-Step Guidance

1. Distribute the multiplication across the coefficients: .

2. Apply the product of powers property to and : .

3. Apply the product of powers property to and .

4. Combine the results, keeping track of negative exponents.

Try solving on your own before revealing the answer!

Q2. Simplify:

Background

Topic: Exponent Rules and Simplifying Rational Expressions

This question tests your ability to use exponent rules to simplify a fraction with negative exponents and variables.

Key Terms and Formulas

• Quotient of Powers:

• Negative Exponent:

• Product Rule:

Step-by-Step Guidance

1. Rewrite $4 to express all terms with base $2$.

2. Combine the exponents for $2.

3. Apply the quotient rule for $2x$ exponents.

4. Subtract exponents in the denominator from those in the numerator for each variable.

Try solving on your own before revealing the answer!

Q3. Simplify:

Background

Topic: Negative Exponents and Simplifying Complex Fractions

This question tests your understanding of negative exponents and how to simplify expressions with exponents in both the numerator and denominator.

Key Terms and Formulas

• Negative Exponent:

• Quotient of Powers:

• Power of a Quotient:

Step-by-Step Guidance

1. Recall that for any nonzero .

2. Simplify the inside of the parentheses: .

3. Apply the quotient rule to exponents: .

4. Apply the negative exponent to the entire fraction.

Try solving on your own before revealing the answer!

Q4. Simplify:

Background

Topic: Scientific Notation and Exponent Rules

This question tests your ability to divide numbers in scientific notation and apply exponent rules.

Key Terms and Formulas

• Scientific Notation:

• Quotient Rule for Exponents:

Step-by-Step Guidance

1. Divide the coefficients: .

2. Apply the exponent rule to .

3. Combine the results to write the answer in scientific notation.

Try solving on your own before revealing the answer!