Evaluating Expressions with Exponents: Assignment

Consider this expression and the steps to evaluate it. 4^5(−2)^9/4^8(−2)^3 1. Apply the quotient of powers: (−2)^a/4^b 2. Evaluate powers: c/d Select the value of each variable. a = b = c = d =

1. 6 2. 3 3. 64 4. 64

Which rules of exponents will be used to evaluate the expression. Check all that apply. (7^5)(7^3)^-4

2. powers of powers 3. power of power 5. negative exponent

Which power does this expression simplify to? ((7^5)(7^3))^-4

A. 1/7^32

Consider the expression. ((2m^-1n^5/3m^0n^4))^2 What is the value of the expression if m = -5 and n = 3?

C. 4/25

Ben simplified this expression. (2x^-4y^7/3x^3y^2)^3 1. (2y^5/3x^7)^5 2. 2y^15/3x^21 Analyze Ben's work. Did he simplify the expression correctly? If not, what was his mistake?

C. No, he needed to apply the exponent to all factors in the product in the second step.

Perform all the steps to evaluate this expression. ((6^7)(3^3)^3/(6^6)(3^4))^3 What is the value of the expression?

D. 8

Tyrone claims that the first step to simplify this expression is to raise the numerator and denominator to the third power. Alisha claims that the first step to simplify is to apply the quotient of powers. Who is correct? Explain.

Sample Answer: Both are correct. Either rule applied first will have the same result. Both rules will be used either way, and the order in which they are applied does not matter as long as they are applied correctly at each step.

Simplify the expression. [(-5)^-7 (-5)^8]^3 1. Apply the product of powers: [(-5)^1]^3 2. Apply the power of a power: (-5)^3 3. Simplify: What is the value of the expression?

-125

Study the expression. What is the value of the expression when m=2 and n= -3? (4m^-3n^2)^2 1. Apply the product of powers: 4^2 m^-6n^4 2. Substitute values for variables: (4)^2(2)^-6(-3)^4 3. Apply the negative exponent: (4)^2(−3)^4/2^6 Complete the steps to evaluate the expression. Written as an improper fraction, the expression has a value of

81/4