Question

Evaluate the following. Check your results by using your calculator. a. \(3+2 \cdot 4 \) b. \(3-2(-4) \) c. \(-2+(2 \cdot 4-3 \cdot 5)\) d. \(3^{2}-5\) e. \(-6^{2}\) f. \((-6)^{2}\) g. \((-2)^{2}+10 \div(-5)\) h. \(12-3^{2}\) i. \(-12 \div 3-4^{2}\) j. \((2 \cdot 3-4 \cdot 5) \div(-2)\) k. \((-13-5) \div 3 \cdot 2 \cdot 1\) l. \(-5+9 \div(8-11)\) m. \(14-(-4)^{2}\) n. \(3-2^{3}\) o. \(3^{2}(-5)^{2} \div(-1)\) j. \((2 \cdot 3-4 \cdot 5) \div(-2)\) k. \((-13-5) \div 3 \cdot 2 \cdot 1\)

Short answer

Question: Evaluate the following expressions using the order of operations: a. \(3+2 \cdot 4\) b. \(3-2(-4)\) c. \(-2+(2 \cdot 4-3 \cdot 5)\) d. \(3^{2}-5\) e. \(-6^{2}\) f. \((-6)^{2}\) g. \((-2)^{2}+10 \div(-5)\) h. \(12-3^{2}\) i. \(-12 \div 3-4^{2}\) j. \((2 \cdot 3-4 \cdot 5) \div(-2)\) k. \((-13-5) \div 3 \cdot 2 \cdot 1\) l. \(-5+9 \div(8-11)\) m. \(14-(-4)^{2}\) n. \(3-2^{3}\) o. \(3^{2}(-5)^{2} \div(-1)\) Answers: a. \(11\) b. \(11\) c. \(-9\) d. \(4\) e. \(-36\) f. \(36\) g. \(2\) h. \(3\) i. \(-20\) j. \(7\) k. \(-12\) l. \(-8\) m. \(-2\) n. \(-5\) o. \(-225\)

Step-by-step solution

Perform multiplication

Evaluate \(2 \cdot 4 = 8\).

Perform addition

Evaluate \(3 + 8 = 11\). Answer: a. \(11\) b. \(3-2(-4)\)

Perform multiplication

Evaluate \(2(-4) = -8\).

Perform subtraction

Evaluate \(3-(-8)=3+8=11\). Answer: b. \(11\) c. \(-2+(2 \cdot 4-3 \cdot 5)\)

Perform multiplication

Evaluate \(2\cdot 4=8\) and \(3\cdot 5=15\).

Perform subtraction within parenthesis

Evaluate \(8-15=-7\).

Perform addition with parenthesis

Evaluate \(-2+(-7)=-9\). Answer: c. \(-9\) d. \(3^{2}-5\)

Evaluate exponent

Evaluate \(3^2 = 9\).

Perform subtraction

Evaluate \(9-5=4\). Answer: d. \(4\) e. \(-6^{2}\)

Evaluate exponent

Evaluate \((-6)^2=36\). Note that the negative sign is not affected. Answer: e. \(-36\) f. \((-6)^{2}\)

Evaluate exponent within parentheses

Evaluate \((-6)^2=36\). Answer: f. \(36\) g. \((-2)^{2}+10 \div(-5)\)

Evaluate exponent and division

Evaluate \((-2)^2=4\) and \(10\div(-5)=-2\).

Perform addition

Evaluate \(4+(-2)=2\). Answer: g. \(2\) h. \(12-3^{2}\)

Evaluate exponent

Evaluate \(3^2=9\).

Perform subtraction

Evaluate \(12-9=3\). Answer: h. \(3\) i. \(-12 \div 3-4^{2}\)

Evaluate division and exponent

Evaluate \(-12 \div 3 = -4\), \(4^2 = 16\).

Perform subtraction

Evaluate \(-4-16=-20\). Answer: i. \(-20\) j. \((2 \cdot 3-4 \cdot 5) \div(-2)\)

Perform multiplication

Evaluate \(2\cdot 3=6\) and \(4\cdot 5=20\).

Perform subtraction within parenthesis

Evaluate \(6-20=-14\).

Perform division with parenthesis

Evaluate \(-14\div(-2)=7\). Answer: j. \(7\) k. \((-13-5) \div 3 \cdot 2 \cdot 1\)

Perform subtraction within parentheses

Evaluate \(-13-5=-18\).

Perform division

Evaluate \(-18 \div 3=-6\).

Perform multiplication

Evaluate \(-6\cdot 2\cdot 1=-12\). Answer: k. \(-12\) l. \(-5+9 \div(8-11)\)

Evaluate subtraction within parentheses

Evaluate \(8-11=-3\).

Evaluate division

Evaluate \(9\div(-3)=-3\).

Perform addition

Evaluate \(-5+(-3)=-8\). Answer: l. \(-8\) m. \(14-(-4)^{2}\)

Evaluate exponent

Evaluate \((-4)^2=16\).

Perform subtraction

Evaluate \(14-16=-2\). Answer: m. \(-2\) n. \(3-2^{3}\)

Evaluate exponent

Evaluate \(2^3=8\).

Perform subtraction

Evaluate \(3-8=-5\). Answer: n. \(-5\) o. \(3^{2}(-5)^{2} \div(-1)\)

Evaluate exponents

Evaluate \(3^2=9\) and \((-5)^2=25\).

Perform multiplication

Evaluate \(9\cdot25=225\).

Perform division

Evaluate \(225\div(-1)=-225\). Answer: o. \(-225\)