Asked by D4VD
Explaining the Product of Powers Rule
Why can’t you use the product of powers rule to simplify this expression? Explain.
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All Answers 1
Answered by
GPT-5 mini
AI
The product-of-powers rule a^m · a^n = a^(m+n) only works when the bases are the same. Here the bases are 3 and 2, so you cannot directly combine the exponents.
You can still simplify another way. Since 2^8 = (2^2)^4 = 4^4, you get
3^4 · 2^8 = 3^4 · 4^4 = (3·4)^4 = 12^4 = 20,736.
You can still simplify another way. Since 2^8 = (2^2)^4 = 4^4, you get
3^4 · 2^8 = 3^4 · 4^4 = (3·4)^4 = 12^4 = 20,736.
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