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 = _
Accepted Solution
A:
Answer:value of a = 6 value of b = 3value of c = 64value of d= 64Step-by-step explanation:1. Apply the quotient of powers:(-2)^a / 4^bIn the given expression:[tex]4^5(-2)^9/4^8(-2)^3[/tex]We know if we have the same base then the powers are subtracting if the bases are in numerator and denominatori.e [tex]a^m/a^n = a^{m-n}[/tex]Solving:[tex]=(-2)^{9-3}/4^{-5+8}\\=(-2)^6/4^3[/tex]So, the value of a = 6 and the value of b = 32. Evaluate Powers c/dWe have [tex](-2)^6/4^3[/tex]Solving:When power is even negative sign changes into plus sign64/64So value of c = 64and value of d= 64