(2^-3x9^3)^-4/2^9x9^-10
To simplify this expression, we can start by expanding the exponents:
(2^-3 * 9^3)^-4 / (2^9 * 9^-10)
= (1/2^3 * 9^3)^-4 / (2^9 * 1/9^10)
= (1/8 * 729)^-4 / (2^9 * 1/9^10)
= (729/8)^-4 / (2^9 / 9^10)
Now, we can simplify the numerator and denominator separately:
Numerator:
(729/8)^-4 = (8/729)^4 = 8^4 / 729^4 = 4096 / 387420489
Denominator:
(2^9 / 9^10) = (2^9 * 9^-10) = 2^9 * 1/9^10 = 512 / 3486784401
Now, we can divide the simplified numerator by the simplified denominator:
(4096 / 387420489) / (512 / 3486784401)
To divide by a fraction, we can multiply by its reciprocal:
(4096 / 387420489) * (3486784401 / 512)
Now, we can simplify this:
(2^12 * 3^12 * 13) / (3^15 * 2^9)
Using the properties of exponents, we can simplify further:
2^(12-9) * 3^(12-15) * 13
= 2^3 * 3^-3 * 13
= 8 / 27 * 13
= 104/27
To simplify the expression (2^-3 * 9^3)^-4 / 2^9 * 9^-10, we can break it down into smaller parts and simplify each part separately.
Step 1: Simplify the numerator.
(2^-3 * 9^3) ^ -4 = (1/(2^3) * (9^3)) ^ -4
= (1/8 * 729) ^ -4
= 9,261 ^ -4
Step 2: Simplify the denominator.
2^9 * 9^-10 = (2^9) / (1/(9^10))
= (2^9) * (9^10)
= 512 * (3^20)
Step 3: Simplify the whole expression.
(9,261^-4) / (512 * 3^20)
At this point, it is difficult to simplify the expression further without knowing specific values or rearranging terms.