How to solve (2^5 )^2 × 7^3 / 8^3 × 7^2 = ?

[@philgreen8101]

k^n * k^m = k^(n + m) => add the exponents k^n / k^m = k^(n - m) => subtract the exponents (k^n)^m = k^(n * m) => multiply the exponents Also factorise values where possible: 8^3 = (2^3)^3 So: (2^5)^2 x 7^3 (2^5)^2 x 7 -------------------- = ----------------- ( 7 ^3 / 7^2 = 7^(3 - 2) = 7^1 = 7, 8^3 x 7^2 (2^3)^3 8 = 2^3) 2^10. x 7 = -------------- ((2^5)^2 = 2^(5 * 2) = 2^10, 2^9 (2^3)^3 = 2^(3 * 3) = 2^9) = 2 x 7 (2^10 / 2^9 = 2^(10 - 9) = 2^1 = 2)