Simplifying Expressions and Exponents

The video tutorial explains how to simplify and evaluate algebraic expressions. It begins with simplifying the expression 36x^5 / 3x^3 by dividing coefficients and subtracting exponents, resulting in 12x^2. The expression is then evaluated by substituting x with 5, yielding a result of 300. A second example is introduced, involving the simplification of a more complex expression with x and y variables. The expression is simplified by applying exponent rules and evaluated by substituting x with -2 and y with -3, resulting in -72. The tutorial concludes with a summary of the steps and concepts covered.

What is the result of simplifying the expression 36 divided by 3 times x to the fifth divided by x to the third?

• 12x^3

• 12x^2

• 12x

• 12x^4

When x equals five, what is the value of the expression 12x^2?

• 300

• 100

• 150

• 200

What is the first step in simplifying the second example expression?

• Eliminate parentheses using power to power property

• Multiply the coefficients

• Divide the coefficients

• Add the exponents

What property is used to eliminate parentheses in the second example?

• Zero exponent

• Quotient of powers

• Product of powers

• Power to power

What is the simplified form of the expression 81x^7y^2 divided by 3^2x^4y^2?

• 9x^6

• 9x^3

• 9x^4

• 9x^5

What happens to the y variable in the second example after simplification?

• It becomes y^1

• It becomes y^2

• It becomes y^0

• It remains unchanged

When x equals negative two, what is the value of the expression 9x^3?

• -72

• 72

• 64

• -64

What is the result of raising negative two to the third power?

• 8

• -8

• 4

• -4

What is the value of y raised to the power of zero?

• 1

• 0

• Undefined

• y

What is the final value of the expression when x equals negative two and y equals negative three?

• 72

• 64

• -64

• -72