Find the value of the following expression:
(2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28
I tried to do a couple steps to solve the question but I don't know if its right.
Step 1:(2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28
Step 2: (2^-16 x 5^-10) x (5^-2/ 2^3)^4 x 2^28
Step 3: (2^-16 x 5^-10) x (5^-8/ 2^12) x 2^26
You lost a minus sign and made a typo. The steps should be
(2^-16 x 5^10) x (5^-2/ 2^3)^4 x 2^28
(2^-16 x 5^10) x (5^-8/ 2^12) x 2^28
Now just collect powers on each base factor.
2^(-16-12+28) x 5^(10-8)
= 5^2
= 25
You made a mistake on step 2. Should be:
Step 1:(2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28
Step 2: (2^-16 x 5^10) x (5^-2/ 2^3)^4 x 2^28
Step 3: (2^-16 x 5^10) x (5^-8/ 2^12) x 2^28
Now expanding out:
Step 4: 2^-16 x 2^12 x 2^28 x 5^10 x 5^-8
Step 5: 2^24 x 5^2
Step 6: 25 x 2^24
Step 7: 25 x 16777216
Step 8: 419430400
Im confused. How did you guys end up with two different answers?
To simplify the given expression:
Step 1: (2^8 x 5^-5 x 19^0)^-2 x (5^-2/ 2^3)^4 x 2^28
Step 2: First, let's simplify the exponents within the parentheses:
2^8 = 256
5^-5 = 1/5^5
19^0 = 1
So the expression becomes:
(256 x (1/5^5) x 1)^-2 x (5^-2/ 2^3)^4 x 2^28
Step 3: Next, let's simplify the exponents outside the parentheses:
(1/5^5)^-2 = (1/(1/5^5))^2 = (1 x 5^5)^2 = 5^10
(5^-2/ 2^3)^4 = (5^-2)^4 / (2^3)^4 = 5^-8 / 2^12 = 1/5^8 x 1/2^12 = 1/(5^8 x 2^12)
2^28 = 2^16 x 2^12 = 65536 x 4096 = 268435456
So the expression becomes:
(5^10) x (1/(5^8 x 2^12)) x 268435456
Step 4: Now, let's simplify the factors:
5^10 = 9765625
(1/(5^8 x 2^12)) = 1/(390625 x 4096) = 1/159252471.04
So the expression simplifies to:
9765625 x (1/159252471.04) x 268435456
Step 5: Finally, let's multiply the factors together to find the value of the expression:
9765625 x (1/159252471.04) x 268435456
= 15625000 / 253084236787374.464
≈ 0.000061743671398039601434
Therefore, the value of the given expression is approximately 0.000061743671398039601434.