Wich of the following is an equivalent expression to (2^-3×9^3)^-4/2^9×9^-10 with only positive exponents, generated by applying the properties of integer exponents

Question

2^-7×9^-1/2^9×9^-10
2^3/9^2
2^3×9^2
2^12×9^-12/2^9×9-10

Answer 1

To simplify the expression and get only positive exponents, we can simplify each term separately and then combine them.

(2^-3×9^3)^-4 = (1/(2^3×9^3))^-4 = (1/(8×(729)))^-4 = 1/(512^4×(531441)^4) = 1/(512^4×531441^4)

2^9×9^-10 = 2^9/(9^10)

Now, let's simplify our expression and combine the terms:

(1/(512^4×531441^4))/(2^9/(9^10))
= (9^10)/(512^4×531441^4)×(1/2^9)
= (3^20)/(2^18×3^36)×(1/2^9)
= (3^20)/(2^18×2^9×3^36)
= (3^20)/(2^27×3^36)
= 3^-7/2^7

Therefore, the equivalent expression with only positive exponents is 3^-7/2^7.