Question

A. Find n so that the number sentence below is true. 2^-6*2^n=2^9.
N=_____________


B. Use the laws of exponents to demonstrate why 2^3•4^3=2^9 is true and explain.

This is true because

Answer 1

n = 15

Step-by-step explanation:

• Step 1: Calculate n by using the law of exponents that a^m × a^n = a^m+n

For 2^-6*2^n=2^9, a = 2, m = -6 and m + n = 9

⇒ -6 + n = 9

⇒ n = 15

• Step 2: Given 2³ × 4³=2^9. Use law of exponents to prove it.

⇒ 2³ × 4³ can also be written as 2³ × (2²)³ = 2³ × 2^6 [This is based on the law of exponents (a^m)^n = (a)^m×n]

⇒ 2³ × 2^6 = 2^ (3 + 6) = 2^9 [Using the law of exponents a^m × a^n = a^m+n]