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# Suppose y=2^x^2+2^x+3. Which of these x-values gives the s

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Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s [#permalink]
Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?
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Re: Suppose y=2^x^2+2^x+3. Which of these x-values gives the s [#permalink]
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PedroBodnar wrote:
Could someone explain me why 2^(-3)^2 does not equal 2^(-6)?

$$a^m^n=a^{(m^n)}$$ and not $$(a^m)^n$$ (if exponentiation is indicated by stacked symbols, the rule is to work from the top down). Thus, $$2^{(-3)^2}=2^{((-3)^2)}=2^9$$ and not $$(2^{(-3)})^2=2^{-6}$$

On the other hand, $$(a^m)^n=a^{mn}$$.

8. Exponents and Roots of Numbers

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