Question

20.) evaluate the given expression using the order of operations. (6³ - 9) ÷ 23 4
21.) simplify the given algebraic expression. 9y + 3r - 5r + 8y
22.) solve the equation. \\(\frac{18 - p}{4} = -4\\)

Explanation:

Question 20: Evaluate \([(6^3 - 9) \div 23]^4\)

Step 1: Calculate \(6^3\)

\(6^3 = 6 \times 6 \times 6 = 216\)

Step 2: Subtract 9 from the result

\(216 - 9 = 207\)

Step 3: Divide by 23

\(207 \div 23 = 9\)

Step 4: Raise to the power of 4

\(9^4 = 9 \times 9 \times 9 \times 9 = 6561\)

Step 1: Combine like terms for \(y\)

\(9y + 8y = (9 + 8)y = 17y\)

Step 2: Combine like terms for \(r\)

\(3r - 5r = (3 - 5)r = -2r\)

Step 3: Combine the results

\(17y - 2r\)

Step 1: Multiply both sides by 4

\(4 \times \frac{18 - p}{4} = -4 \times 4\)
\(18 - p = -16\)

Step 2: Subtract 18 from both sides

\(18 - p - 18 = -16 - 18\)
\(-p = -34\)

Step 3: Multiply both sides by -1

\(p = 34\)

Answer:

\(6561\)

Question 21: Simplify \(9y + 3r - 5r + 8y\)