Answer:
5. 2¯⁶ or 1/2⁶
6. 2⁹
Explanation:
5. Simplify 2⁴ ÷ 2¹⁰
The above expression can be simplified as follow:
2⁴ ÷ 2¹⁰
Recall
Aⁿ ÷ Aᵐ = Aⁿ¯ᵐ
Thus,
2⁴ ÷ 2¹⁰ = 2⁴ ¯ ¹⁰
2⁴ ÷ 2¹⁰ = 2¯⁶
Recall:
A¯ⁿ = 1/Aⁿ
Thus,
2¯⁶ = 1/2⁶
Therefore,
2⁴ ÷ 2¹⁰ = 2¯⁶ or 1/2⁶
6. Simplify 2³ × (2²)³
2³ × (2²)³ can be simplified as follow:
2³ × (2²)³
Recall
(Aⁿ)ᵐ = Aⁿ*ᵐ
Thus,
(2²)³ = 2²*³
(2²)³ = 2⁶
2³ × (2²)³ = 2³ × 2⁶
Recall
Aⁿ × Aᵐ = Aⁿ⁺ᵐ
2³ × 2⁶ = 2³⁺⁶
2³ × 2⁶ = 2⁹
Therefore,
2³ × (2²)³ = 2⁹