If \(4^{3} \times 5^6 = 10^m\), then find the value of \(m\).
6
6 is correct.
Write 4 as a power of 2: \(4^3 = (2^2)^3 = 2^6\).
So the left side becomes \(2^6 \times 5^6 = (2 \times 5)^6 = 10^6\), using the rule \(a^n \times b^n = (ab)^n\).
Since the exponents are now equal, the two bases can be combined into one power of 10.
Comparing \(10^6 = 10^m\) gives \(m = 6\).
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