Problem

Problem

Write 83x×162x−18^{3x} \times 16^{2x-1} as a power of 2.
Intuitive explanation

The key is to rewrite both bases as powers of 2, then use exponent rules to combine them. Since 8=238 = 2^3 and 16=2416 = 2^4, you can substitute these in and apply the power rule (am)n=amn(a^m)^n = a^{mn} to each term. Once everything is expressed as a single power of 2, you'll add the exponents together.

Intuitive explanation

The key is to rewrite both bases as powers of 2, then use exponent rules to combine them. Since 8=238 = 2^3 and 16=2416 = 2^4, you can substitute these in and apply the power rule (am)n=amn(a^m)^n = a^{mn} to each term. Once everything is expressed as a single power of 2, you'll add the exponents together.

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