EXERCISE 2.9 Calculators may not be used in this exercise. (a) Calculate: $$ \begin{array}{llll} ext { (1) } 2^{2} & ext { (2) } 7^{2} & ext { (3) } 8^{2} \ ext { (4) } 10^{3} & ext { (5) } 1^{2}+1^{3} & ext { (6) } 0^{2}+0^{3} \ ext { (7) }(-5)^{2} & ext { (8) }-5^{2} & ext { (9) }(-5)^{3} \ ext { (10) }-5^{3} & ext { (11) }-(-5)^{2} & ext { (12) }-(-5)^{3} \ ext { (13) } 9^{2}+9^{3} & ext { (14) }(-12)^{2}+(-2)^{3} & ext { (15) } 15^{2}-(-11)^{2}\end{array} $$

Question

EXERCISE 2.9 Calculators may not be used in this exercise. (a) Calculate: $$ \begin{array}{llll}	ext { (1) } 2^{2} & 	ext { (2) } 7^{2} & 	ext { (3) } 8^{2} \ 	ext { (4) } 10^{3} & 	ext { (5) } 1^{2}+1^{3} & 	ext { (6) } 0^{2}+0^{3} \ 	ext { (7) }(-5)^{2} & 	ext { (8) }-5^{2} & 	ext { (9) }(-5)^{3} \ 	ext { (10) }-5^{3} & 	ext { (11) }-(-5)^{2} & 	ext { (12) }-(-5)^{3} \ 	ext { (13) } 9^{2}+9^{3} & 	ext { (14) }(-12)^{2}+(-2)^{3} & 	ext { (15) } 15^{2}-(-11)^{2}\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's work through each of the calculations step by step.

### (a) Calculate:

#### (1) $$ 2^{2} $$
$$
2^{2} = 2 \times 2 = 4
$$

#### (2) $$ 7^{2} $$
$$
7^{2} = 7 \times 7 = 49
$$

#### (3) $$ 8^{2} $$
$$
8^{2} = 8 \times 8 = 64
$$

#### (4) $$ 10^{3} $$
$$
10^{3} = 10 \times 10 \times 10 = 1000
$$

#### (5) $$ 1^{2} + 1^{3} $$
$$
1^{2} = 1 \times 1 = 1
$$
$$
1^{3} = 1 \times 1 \times 1 = 1
$$
$$
1^{2} + 1^{3} = 1 + 1 = 2
$$

#### (6) $$ 0^{2} + 0^{3} $$
$$
0^{2} = 0 \times 0 = 0
$$
$$
0^{3} = 0 \times 0 \times 0 = 0
$$
$$
0^{2} + 0^{3} = 0 + 0 = 0
$$

#### (7) $$ (-5)^{2} $$
$$
(-5)^{2} = (-5) \times (-5) = 25
$$

#### (8) $$ -5^{2} $$
**Important:** The placement of the negative sign matters.
$$
-5^{2} = -(5 \times 5) = -25
$$

#### (9) $$ (-5)^{3} $$
$$
(-5)^{3} = (-5) \times (-5) \times (-5) = -125
$$

#### (10) $$ -5^{3} $$
Again, pay attention to the negative sign placement.
$$
-5^{3} = -(5 \times 5 \times 5) = -125
$$

#### (11) $$ -(-5)^{2} $$
$$
(-5)^{2} = (-5) \times (-5) = 25
$$
$$
-(-5)^{2} = -25
$$

#### (12) $$ -(-5)^{3} $$
$$
(-5)^{3} = (-5) \times (-5) \times (-5) = -125
$$
$$
-(-5)^{3} = 125
$$

#### (13) $$ 9^{2} + 9^{3} $$
$$
9^{2} = 9 \times 9 = 81
$$
$$
9^{3} = 9 \times 9 \times 9 = 729
$$
$$
9^{2} + 9^{3} = 81 + 729 = 810
$$

#### (14) $$ (-12)^{2} + (-2)^{3} $$
$$
(-12)^{2} = (-12) \times (-12) = 144
$$
$$
(-2)^{3} = (-2) \times (-2) \times (-2) = -8
$$
$$
(-12)^{2} + (-2)^{3} = 144 + (-8) = 136
$$

#### (15) $$ 15^{2} - (-11)^{2} $$
$$
15^{2} = 15 \times 15 = 225
$$
$$
(-11)^{2} = (-11) \times (-11) = 121
$$
$$
15^{2} - (-11)^{2} = 225 - 121 = 104
$$

### Summary of Answers:

1. $$ 2^{2} = 4 $$
2. $$ 7^{2} = 49 $$
3. $$ 8^{2} = 64 $$
4. $$ 10^{3} = 1000 $$
5. $$ 1^{2} + 1^{3} = 2 $$
6. $$ 0^{2} + 0^{3} = 0 $$
7. $$ (-5)^{2} = 25 $$
8. $$ -5^{2} = -25 $$
9. $$ (-5)^{3} = -125 $$
10. $$ -5^{3} = -125 $$
11. $$ -(-5)^{2} = -25 $$
12. $$ -(-5)^{3} = 125 $$
13. $$ 9^{2} + 9^{3} = 810 $$
14. $$ (-12)^{2} + (-2)^{3} = 136 $$
15. $$ 15^{2} - (-11)^{2} = 104 $$

If you have any further questions or need additional explanations for any of these calculations, feel free to ask!
Here are the answers to the calculations: 1. $$ 2^{2} = 4 $$ 2. $$ 7^{2} = 49 $$ 3. $$ 8^{2} = 64 $$ 4. $$ 10^{3} = 1000 $$ 5. $$ 1^{2} + 1^{3} = 2 $$ 6. $$ 0^{2} + 0^{3} = 0 $$ 7. $$ (-5)^{2} = 25 $$ 8. $$ -5^{2} = -25 $$ 9. $$ (-5)^{3} = -125 $$ 10. $$ -5^{3} = -125 $$ 11. $$ -(-5)^{2} = -25 $$ 12. $$ -(-5)^{3} = 125 $$ 13. $$ 9^{2} + 9^{3} = 810 $$ 14. $$ (-12)^{2} + (-2)^{3} = 136 $$ 15. $$ 15^{2} - (-11)^{2} = 104 $$

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