Question

solve for the varaiables shown in the steps simplifiying the expression below: 2^5 × 8^4/16 = 2^5 × (2^a)^4/2^4 = 2^5 × 2^b/2^4 = 2^c

Answer 1

given the expresions

Solving a

$\frac{2^5*8^4}{16}=\frac{2^5*(2^a)^4}{2^4}$$\frac{8^4}{16}=\frac{(2^a)^4}{2^4}$$\frac{8^4}{16}=\frac{(2^a)^4}{16}$$8^4=(2^a)^4$$8=(2^a)$$a=3$

Solving b

$\frac{2^5\cdot8^4}{16}=\frac{2^5*2^b}{2^4}$$\frac{2^5\cdot8^4}{16}=\frac{2^5*2^b}{16}$$2^5\cdot8^4=2^5*2^b$$8^4=2^b$$((2)^3)^4=2^b$$2^{12}=2^b$$b=12$

solving C

$\:\frac{2^5\cdot8^4}{16}=2^c$$\:\frac{2^5\cdot2^{12}}{2^4}=2^c$$\:\frac{2^{(5+12)}}{2^4}=2^c$$\:\frac{2^{(17)}}{2^4}=2^c$$\:2^{(17-4)}=2^c$$\:2^{(13)}=2^c$$C=13$

then

A=3

B=12

C=13