Question:
Geoffrey is evaluating the expression (-3)^3(2^6)/(-3)^5(2^2) as shown below.
(-3)^3(2^6)/(-3)^5(2^2) = (2)^a/(-3)^b = c/d
What are the values of a, b, c, and d?
Answer:
The values are a = 4, b = 2, c = 16, d = 9
Solution:
Given that,
Geoffrey is evaluating the expression
[tex]\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2}[/tex]
He is evaluating as shown below:
[tex]\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^a}{-3^b} = \frac{c}{d}[/tex]
From given,
[tex]\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2}[/tex]
Use the law of exponent
[tex]\frac{a^m}{a^n} = a^{m - n}[/tex]
Therefore,
[tex]\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^{6-2}}{(-3)^{5-3}}\\\\Simplify\\\\\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^4}{-3^2}[/tex]
Thus,
a = 4
b = 2
Simplify further
[tex]\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^4}{-3^2} = \frac{16}{9}[/tex]
Thus,
c = 16
d = 9
Thus values are a = 4, b = 2, c = 16, d = 9
