Answer:
a = 6
b = 3
c = 64
d= 64
Step-by-step explanation:
1. Apply the quotient of powers:
[tex](-2)^a / 4^b[/tex]
In the given expression:
[tex]4^5(-2)^9/4^8(-2)^3[/tex]
base same then the powers are subtracting if the bases are in numerator and denominator
i.e [tex]a^m/a^n = a^{m-n}[/tex]
Solving:
[tex]=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3[/tex]
therefore, the values of a and b are: a = 6
b = 3
2. Evaluate Powers
c/d
We have
[tex](-2)^6/4^3[/tex]
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
