Question

Consider this expression and the steps to evaluate it.
4^5(−2)^9/4^8(−2)^3
1. Apply the quotient of powers:     (−2)^a/4^b

2. Evaluate powers:          c/d

Select the value of each variable.
a = _
b = _
c = _
d = _

Answer 1

Answer:

value of a = 6

value of b = 3

value of c = 64

value of d= 64

Step-by-step explanation:

1. Apply the quotient of powers:

(-2)^a / 4^b

In the given expression:

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

We know if we have the same base then the powers are subtracting if the bases are in numerator and denominator

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

Solving:

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

So, the value of a = 6

and the value of b = 3

2. Evaluate Powers

c/d

We have

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

Solving:

When power is even negative sign changes into plus sign

64/64

So value of c = 64

and value of d= 64

Answer 2

Answer:

a=6

b=3

c=64

d=64

Step-by-step explanation: