What is (2^a)/((2^b))=256,2^a*2^b=1 ?

The solution to (2^a)/((2^b))=256,2^a*2^b=1 is

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(2^a)/((2^b))=256,2^a*2^b=1

\frac{2 ^{a}}{( 2 ^{b} )} = 256, 2^{a} \cdot 2^{b} = 1

(a = 4, b = - 4)

Solution steps

[\frac{2 ^{a}}{( 2 ^{b} )} = 256 2^{a} \cdot 2^{b} = 1]

Isolate

2^{a}

for

\frac{2 ^{a}}{( 2 ^{b} )} = 256 : 2^{a} = 2^{8 + b}

Plug the solutions

2^{a} = 2^{8 + b}

into

2^{a} \cdot 2^{b} = 1

For

2^{a} \cdot 2^{b} = 1

, subsitute

2^{a}

with

2^{8 + b} : b = - 4

Plug the solutions

b = - 4

into

\frac{2 ^{a}}{( 2 ^{b} )} = 256

For

\frac{2 ^{a}}{( 2 ^{b} )} = 256

, subsitute

b

with

- 4 : a = 4

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{2 ^{a}}{( 2 ^{b} )} = 256, 2^{a} \cdot 2^{b} = 1

(a = 4, b = - 4)

9 x + 14 y = 83, 39 x - 35 y = - 23

4 x + 2 y = 5, 3 x + 6 y = 6

x + y + 2 z = - 1, 2 x - y + 2 z = - 4, 4 x + y + 4 z = - 2

63 x - 14 y = 75, 66 x + 14 y = 210

9 x + 6 y = 51, 14 x - 7 y = 14

What is (2^a)/((2^b))=256,2^a*2^b=1 ?
The solution to (2^a)/((2^b))=256,2^a*2^b=1 is