Question

this is the complete order of operations hierarchy. grouping exponents multiplication & division from left to right addition & subtraction from left to right now we are going to work on the third level from the bottom, as promised earlier exponents: let’s review exponents and how to evaluate them. base →2^3 ←exponent what does this mean? 2^3 = 2·2·2 2^3 = 2^3 = evaluate the following exponents. ex 1. 7^2 = ex 2. 3^4 = ex 3. 5^3 = ex 4. (-7)^2 = ex 5. (-3)^4 = ex 6. (-5)^3 = ex 7. (-4)^3 = ex 8. (-2)^4 ex 9. (-2)^5

Explanation:

Step1: Recall exponent - calculation rule

The rule for calculating \(a^n\) is \(a\times a\times\cdots\times a\) (\(n\) times).

Step2: Calculate \(7^2\)

\(7^2=7\times7 = 49\)

Step3: Calculate \(3^4\)

\(3^4=3\times3\times3\times3=81\)

Step4: Calculate \(5^3\)

\(5^3=5\times5\times5 = 125\)

Step5: Calculate \((-7)^2\)

\((-7)^2=(-7)\times(-7)=49\)

Step6: Calculate \((-3)^4\)

\((-3)^4=(-3)\times(-3)\times(-3)\times(-3)=81\)

Step7: Calculate \((-5)^3\)

\((-5)^3=(-5)\times(-5)\times(-5)=- 125\)

Step8: Calculate \((-4)^3\)

\((-4)^3=(-4)\times(-4)\times(-4)=-64\)

Step9: Calculate \((-2)^4\)

\((-2)^4=(-2)\times(-2)\times(-2)\times(-2)=16\)

Step10: Calculate \((-2)^5\)

\((-2)^5=(-2)\times(-2)\times(-2)\times(-2)\times(-2)=-32\)

Answer:

Ex 1. \(49\)
Ex 2. \(81\)
Ex 3. \(125\)
Ex 4. \(49\)
Ex 5. \(81\)
Ex 6. \(-125\)
Ex 7. \(-64\)
Ex 8. \(16\)
Ex 9. \(-32\)