Q1. Find the value of the expression .

Background

Topic: Exponents

This question tests your understanding of exponent rules and evaluating expressions with exponents.

Key Terms and Formulas:

• Exponent: The number that indicates how many times to multiply the base by itself.

• means multiply by itself times.

Step-by-Step Guidance

1. First, evaluate the expression inside the exponent: .

2. Substitute the result into the exponent: becomes .

3. Recall that any number to the first power is itself: .

Try solving on your own before revealing the answer!

Q2. Simplify the inequality to determine whether it is true or false: .

Background

Topic: Inequalities and Order of Operations

This question tests your ability to simplify expressions using the order of operations and compare values using inequalities.

Key Terms and Formulas:

• Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction)

• Inequality: A mathematical statement that compares two values.

Step-by-Step Guidance

1. Simplify inside the parentheses: .

2. Multiply the result by 5: .

3. Compare the final value to 80 using the symbol.

Try solving on your own before revealing the answer!

Q3. Simplify the following:

Background

Topic: Combining Like Terms and Simplifying Rational Expressions

This question tests your ability to combine like terms in the numerator and simplify the resulting fraction.

Key Terms and Formulas:

• Like Terms: Terms that have the same variable raised to the same power.

• Rational Expression: A fraction where the numerator and denominator are polynomials.

Step-by-Step Guidance

1. Combine all the terms in the numerator: .

2. Write the simplified numerator over the denominator .

3. Check if the fraction can be simplified further.

Try solving on your own before revealing the answer!

Q4. Evaluate the following for and :

Background

Topic: Substitution and Evaluation of Expressions

This question tests your ability to substitute values for variables and evaluate the resulting expression.

Key Terms and Formulas:

• Substitution: Replacing variables with their given values.

• Evaluation: Calculating the value of an expression.

Step-by-Step Guidance

1. Substitute and into the expression: .

2. Add the values inside the parentheses: .

3. Multiply the result by 7.

4. Divide the result by 6.

Try solving on your own before revealing the answer!

Q5. Find the value of the expression .

Background

Topic: Exponents and Simplifying Fractions

This question tests your ability to evaluate exponents and simplify fractions.

Key Terms and Formulas:

• Exponent: means multiply by itself times.

• Simplifying Fractions: Reduce the fraction to lowest terms if possible.

Step-by-Step Guidance

1. Evaluate and separately.

2. Write the fraction with the evaluated numerator and denominator.

3. Check if the fraction can be simplified further.

Try solving on your own before revealing the answer!