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Is 2^{3} × 2 equal to 2^{2} × 2^{2} × 2^{2}?

Answer

No, 2^{3} × 2 equals 2^{4} and 2^{2} × 2^{2} × 2^{2 }equals 2^{6}.

What is (4^{3} × 4^{5})^{2}?

Hint

Don't forget to use the order of operations.

(4^{3} × 4^{5})^{2} = (4^{8})^{2} = 4^{16}.

Does (a^{b})^{c} = a(b^{c})?

No way. The multiplicative rule says that (a^{b})^{c} = a^{bc}. Since bc ≠ b^{c}, these are not the same.