Question

(-3)3 (26)

Answer 1

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

$\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2}$

He is evaluating as shown below:

$\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^a}{-3^b} = \frac{c}{d}$

From given,

$\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2}$

Use the law of exponent

$\frac{a^m}{a^n} = a^{m - n}$

Therefore,

$\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^{6-2}}{(-3)^{5-3}}\\\\Simplify\\\\\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^4}{-3^2}$

Thus,

a = 4

b = 2

Simplify further

$\frac{(-3)^3 \times 2^6}{(-3)^5 \times 2^2} = \frac{2^4}{-3^2} = \frac{16}{9}$

Thus,

c = 16

d = 9

Thus values are a = 4, b = 2, c = 16, d = 9