If m and n are natural numbers such that n > 1, and m^n = 2^{25} × 3^{40}, then m − n equals
Question:
If m and n are natural numbers such that n > 1, and m^n = 2^{25} × 3^{40}, then m − n equals
If m and n are natural numbers such that n > 1, and m^n = 2^{25} × 3^{40}, then m − n equals
Options
Answer: 209947
Explanation:
Write exponents with a common factor: 2^{25} × 3^{40} = (2^5)^{5} × (3^8)^{5} = (2^5 × 3^8)^5. So n = 5 and m = 2^5 × 3^8 = 32 × 6561 = 209952. Therefore m − n = 209952 − 5 = 209947.
Explanation:
Write exponents with a common factor: 2^{25} × 3^{40} = (2^5)^{5} × (3^8)^{5} = (2^5 × 3^8)^5. So n = 5 and m = 2^5 × 3^8 = 32 × 6561 = 209952. Therefore m − n = 209952 − 5 = 209947.
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