Question

18.) simplify the given numerical expression in the space provided. then choose words from the word bank that explain what you did at each step. \\( 7 - 3(5^3 + 1) \div 6 \\) word bank subtract divide add simplify the power multiply steps followed a.) simplify the power (because) ( ) b.) add ( ) ( ) c.) multiply ( ) ( ) d.) divide ( ) ( ) e.) subtract ( ) ( ) 19.) evaluate the given expression using the order of operations. \\( 4^3 \div 2 - 3(4) \\)

Explanation:

Problem 18: Simplify \( 7 - 3(5^3 + 1) \div 6 \)

Step 1: Simplify the power (inside parentheses)

First, we simplify the exponent \( 5^3 \). By the definition of exponents, \( 5^3 = 5 \times 5 \times 5 = 125 \). So the expression inside the parentheses becomes \( 125 + 1 \).
Expression: \( 7 - 3(125 + 1) \div 6 \)

Step 2: Add (inside parentheses)

Now, we add the numbers inside the parentheses: \( 125 + 1 = 126 \).
Expression: \( 7 - 3(126) \div 6 \)

Step 3: Multiply (outside parentheses)

Next, we multiply \( 3 \) and \( 126 \): \( 3 \times 126 = 378 \).
Expression: \( 7 - 378 \div 6 \)

Step 4: Divide

Now, we perform the division: \( 378 \div 6 = 63 \).
Expression: \( 7 - 63 \)

Step 5: Subtract

Finally, we subtract: \( 7 - 63 = -56 \).
Expression: \( -56 \)

Step 1: Simplify the power

First, we simplify the exponent \( 4^3 \). By the definition of exponents, \( 4^3 = 4 \times 4 \times 4 = 64 \).
Expression: \( 64 \div 2 - 3(4) \)

Step 2: Divide

Next, we perform the division: \( 64 \div 2 = 32 \).
Expression: \( 32 - 3(4) \)

Step 3: Multiply

Now, we multiply \( 3 \) and \( 4 \): \( 3 \times 4 = 12 \).
Expression: \( 32 - 12 \)

Step 4: Subtract

Finally, we subtract: \( 32 - 12 = 20 \).
Expression: \( 20 \)

Answer:

The simplified value of \( 7 - 3(5^3 + 1) \div 6 \) is \(-56\).

Problem 19: Evaluate \( 4^3 \div 2 - 3(4) \)