Question

iv. evalúe cada expresión pasos en libreta

1. $4^2 + 2^3 - 2^2 - 3^2 = 16 + 8 - 4 - 9 = 11$
2. $(-1)^2 + (-1)^3 - 1^4 + 1^5 = 0$
3. $-2^2 - 2^3 + 1^{10} + (-2)^3 = -19$
4. $(-3)^3 - 2^2 - (-2)^2 + (6 - 6)^2 = -35$
5. $(1.5)^2 - (3.9)^2 + (-2.1)^3 = -22.221$
6. $3^2 + (-4)^3 - 5^2 = -80$
7. $6^2 - (-2)^3 = 44$
8. $4^2 + -1(3 + 2)^3 = -109$
9. $(3 + 5)^4 = 4096$
10. ${3 + 2-4 + 1(3)}^2 = 1$

Explanation:

To solve these expressions, we follow the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). Let's solve each expression one by one:

1. \(4^2 + 2^3 - 2^2 - 3^2\)

Step 1: Calculate the exponents

\(4^2 = 16\), \(2^3 = 8\), \(2^2 = 4\), \(3^2 = 9\)

Step 2: Substitute the values and simplify

\(16 + 8 - 4 - 9 = 24 - 4 - 9 = 20 - 9 = 11\)

2. \((-1)^2 + (-1)^3 - 1^4 + 1^5\)

Step 1: Calculate the exponents

\((-1)^2 = 1\), \((-1)^3 = -1\), \(1^4 = 1\), \(1^5 = 1\)

Step 2: Substitute the values and simplify

\(1 + (-1) - 1 + 1 = 0 - 1 + 1 = 0\)

3. \(-2^2 - 2^3 + 1^{10} + (-2)^3\)

Step 1: Calculate the exponents

\(-2^2 = -4\) (note: exponentiation first, then negation), \(2^3 = 8\), \(1^{10} = 1\), \((-2)^3 = -8\)

Step 2: Substitute the values and simplify

\(-4 - 8 + 1 + (-8) = -12 + 1 - 8 = -11 - 8 = -19\)

4. \((-3)^3 - 2^2 - (-2)^2 + (6 - 6)^2\)

Step 1: Calculate the exponents and parentheses

\((-3)^3 = -27\), \(2^2 = 4\), \((-2)^2 = 4\), \((6 - 6)^2 = 0^2 = 0\)

Step 2: Substitute the values and simplify

\(-27 - 4 - 4 + 0 = -31 - 4 + 0 = -35\)

5. \((1.5)^2 - (3.9)^2 + (-2.1)^3\)

Step 1: Calculate the exponents

\((1.5)^2 = 2.25\), \((3.9)^2 = 15.21\), \((-2.1)^3 = -9.261\)

Step 2: Substitute the values and simplify

\(2.25 - 15.21 + (-9.261) = -12.96 - 9.261 = -22.221\)

6. \(3^2 + (-4)^3 - 5^2\)

Step 1: Calculate the exponents

\(3^2 = 9\), \((-4)^3 = -64\), \(5^2 = 25\)

Step 2: Substitute the values and simplify

\(9 + (-64) - 25 = -55 - 25 = -80\)

7. \(6^2 - (-2)^3\)

Step 1: Calculate the exponents

\(6^2 = 36\), \((-2)^3 = -8\)

Step 2: Substitute the values and simplify

\(36 - (-8) = 36 + 8 = 44\)

8. \(4^2 + [-1(3 + 2)]^3\)

Step 1: Calculate inside the brackets and exponents

First, \(3 + 2 = 5\), then \(-1(5) = -5\), \(4^2 = 16\), \((-5)^3 = -125\)

Step 2: Substitute the values and simplify

\(16 + (-125) = -109\)

9. \((3 + 5)^4\)

Step 1: Calculate inside the parentheses and exponent

\(3 + 5 = 8\), \(8^4 = 4096\)

Step 2: Substitute the values and simplify

\(4096\)

10. \(\{3 + 2[-4 + 1(3)]\}^2\)

Step 1: Calculate inside the innermost parentheses

\(1(3) = 3\), then \(-4 + 3 = -1\)

Step 2: Calculate inside the brackets

\(2(-1) = -2\), then \(3 + (-2) = 1\)

Step 3: Calculate the exponent

\(1^2 = 1\)

Step 4: Substitute the values and simplify

\(1\)

Resumen de Respuestas:

1. \(11\)
2. \(0\)
3. \(-19\)
4. \(-35\)
5. \(-22.221\)
6. \(-80\)
7. \(44\)
8. \(-109\)
9. \(4096\)
10. \(1\)

Answer:

To solve these expressions, we follow the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). Let's solve each expression one by one:

1. \(4^2 + 2^3 - 2^2 - 3^2\)

Step 1: Calculate the exponents

\(4^2 = 16\), \(2^3 = 8\), \(2^2 = 4\), \(3^2 = 9\)

Step 2: Substitute the values and simplify

\(16 + 8 - 4 - 9 = 24 - 4 - 9 = 20 - 9 = 11\)

2. \((-1)^2 + (-1)^3 - 1^4 + 1^5\)

Step 1: Calculate the exponents

\((-1)^2 = 1\), \((-1)^3 = -1\), \(1^4 = 1\), \(1^5 = 1\)

Step 2: Substitute the values and simplify

\(1 + (-1) - 1 + 1 = 0 - 1 + 1 = 0\)

3. \(-2^2 - 2^3 + 1^{10} + (-2)^3\)

Step 1: Calculate the exponents

\(-2^2 = -4\) (note: exponentiation first, then negation), \(2^3 = 8\), \(1^{10} = 1\), \((-2)^3 = -8\)

Step 2: Substitute the values and simplify

\(-4 - 8 + 1 + (-8) = -12 + 1 - 8 = -11 - 8 = -19\)

4. \((-3)^3 - 2^2 - (-2)^2 + (6 - 6)^2\)

Step 1: Calculate the exponents and parentheses

\((-3)^3 = -27\), \(2^2 = 4\), \((-2)^2 = 4\), \((6 - 6)^2 = 0^2 = 0\)

Step 2: Substitute the values and simplify

\(-27 - 4 - 4 + 0 = -31 - 4 + 0 = -35\)

5. \((1.5)^2 - (3.9)^2 + (-2.1)^3\)

Step 1: Calculate the exponents

\((1.5)^2 = 2.25\), \((3.9)^2 = 15.21\), \((-2.1)^3 = -9.261\)

Step 2: Substitute the values and simplify

\(2.25 - 15.21 + (-9.261) = -12.96 - 9.261 = -22.221\)

6. \(3^2 + (-4)^3 - 5^2\)

Step 1: Calculate the exponents

\(3^2 = 9\), \((-4)^3 = -64\), \(5^2 = 25\)

Step 2: Substitute the values and simplify

\(9 + (-64) - 25 = -55 - 25 = -80\)

7. \(6^2 - (-2)^3\)

Step 1: Calculate the exponents

\(6^2 = 36\), \((-2)^3 = -8\)

Step 2: Substitute the values and simplify

\(36 - (-8) = 36 + 8 = 44\)

8. \(4^2 + [-1(3 + 2)]^3\)

Step 1: Calculate inside the brackets and exponents

First, \(3 + 2 = 5\), then \(-1(5) = -5\), \(4^2 = 16\), \((-5)^3 = -125\)

Step 2: Substitute the values and simplify

\(16 + (-125) = -109\)

9. \((3 + 5)^4\)

Step 1: Calculate inside the parentheses and exponent

\(3 + 5 = 8\), \(8^4 = 4096\)

Step 2: Substitute the values and simplify

\(4096\)

10. \(\{3 + 2[-4 + 1(3)]\}^2\)

Step 1: Calculate inside the innermost parentheses

\(1(3) = 3\), then \(-4 + 3 = -1\)

Step 2: Calculate inside the brackets

\(2(-1) = -2\), then \(3 + (-2) = 1\)

Step 3: Calculate the exponent

\(1^2 = 1\)

Step 4: Substitute the values and simplify

\(1\)

Resumen de Respuestas:

1. \(11\)
2. \(0\)
3. \(-19\)
4. \(-35\)
5. \(-22.221\)
6. \(-80\)
7. \(44\)
8. \(-109\)
9. \(4096\)
10. \(1\)