Question

Consider this expression and the steps to evaluate it. 45(−2)9 48(−2)3 1. Apply the quotient of powers: (−2)a 4b 2. Evaluate powers: c d

Answer 1

Answer:

a = 6

b = 3

c = 64

d= 64

Step-by-step explanation:

1. Apply the quotient of powers:

$(-2)^a / 4^b$

In the given expression:

$4^5(-2)^9/4^8(-2)^3$

base same then the powers are subtracting if the bases are in numerator and denominator

i.e $a^m/a^n = a^{m-n}$

Solving:

$=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3$

therefore, the values of a and b are: a = 6

b = 3

2. Evaluate Powers

c/d

We have

$(-2)^6/4^3$

When power is even negative sign changes into plus sign

64/64

Therefore, we get the values of c and d

c = 64

d= 64