1. Evaluate the following expression using laws of expression:
a) 2−2 × 56 × 72 ×114
b) 2−2 ×72 × 114
c) 2−2 × 56 ×114
d) 2−5 × 56 ×72 ×114
Answer: c) 2−2 × 56 × 114
Explanation: Using laws of exponents,
2. Which is the following numerical expression in scientific notation “A single drop of water has 60230000000000000000000 molecules.”?
a) 023 × 1019 molecules
b) 023 × 1021 molecules
c) 023 × 1022 molecules
d) 023 × 1023 molecules
Answer: c) 6.023 × 1022 molecules
Explanation:
3. What is the value of “a” in the given equation?
(202311)a ÷ (20237)a = (2023)108
a) 21
b) 23
c) 27
d) 29
Answer: c) 27
Explanation: Using laws of exponents,
(202311)a ÷ (20237)a = (2023)108
⇒ (2023)11×a ÷ (2023)7×a = (2023)108
⇒ (2023)11a ÷ (2023)7a = (2023)108
⇒ (2023)11a − 7a = (2023)108
⇒ (2023)4a = (2023)108
Comparing both sides
⇒ 4a = 108
⇒ a = 108/4
⇒ a = 27
4. What is the value of n in the following equation?
a) −3
b) 3
c) −5
d) 5
Answer: b) 3
Explanation: Using laws of exponents,
Comparing both sides
⇒ n = 3
5. Simplify the following expression using laws of exponents:
(−1)199 ×[(243)3 ÷ (27)4]
a) −27
b) 2
c) −81
d) 81
Answer: a) −27
Explanation: Using laws of exponents,
(−1)199 × [(243)3 ÷ (27)4]
= (−1) × [(35)3 ÷ (33)4] [(−1)odd = −1]
= (−1) × [315 ÷ 312]
= (−1) × [315 − 12]
= (−1) × [33]
= (−1) × 27
= −27
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