Answer:
2¹⁶ⁿ
Step-by-step explanation:
2ⁿ¯⁴ × 16¹⁺ⁿ / 8¯ⁿ × 4¯⁴ⁿ
The above expression can be simplified as follow:
2ⁿ¯⁴ × 16¹⁺ⁿ / 8¯ⁿ × 4¯⁴ⁿ
Recall:
16 = 2⁴
8 = 2³
4 = 2²
Thus,
2ⁿ¯⁴ × 16¹⁺ⁿ / 8¯ⁿ × 4¯⁴ⁿ
= 2ⁿ¯⁴ × 2⁴⁽¹⁺ⁿ⁾ / 2³⁽¯ⁿ⁾ × 2²⁽¯⁴ⁿ⁾
= 2ⁿ¯⁴ × 2⁴⁺⁴ⁿ / 2¯³ⁿ × 2¯⁸ⁿ
Recall:
Mᵃ × Mᵇ = Mᵃ⁺ᵇ
2ⁿ¯⁴ × 2⁴⁺⁴ⁿ / 2¯³ⁿ × 2¯⁸ⁿ
= 2⁽ⁿ¯⁴⁾⁺⁽⁴⁺⁴ⁿ⁾ / 2¯³ⁿ⁺⁽¯⁸ⁿ⁾
= 2ⁿ¯⁴⁺⁴⁺⁴ⁿ/ 2¯³ⁿ¯⁸ⁿ
= 2⁵ⁿ / 2¯¹¹ⁿ
Recall:
Mᵃ / Mᵇ = Mᵃ¯ᵇ
2⁵ⁿ / 2¯¹¹ⁿ = 2⁵ⁿ¯⁽¯¹¹ⁿ⁾
2⁵ⁿ / 2¯¹¹ⁿ = 2⁵ⁿ⁺¹¹ⁿ
2⁵ⁿ / 2¯¹¹ⁿ = 2¹⁶ⁿ
Therefore,
2ⁿ¯⁴ × 16¹⁺ⁿ / 8¯ⁿ × 4¯⁴ⁿ = 2¹⁶ⁿ