Question

Exponents and Powers Question
Need help, please answer with explanation.

Answer 1

a = -1

Explanation:

The sign of a number raised to an even power is irrelevant. That means we can rewrite (-25)² as (-5)⁴. Doing so lets us combine the factors like so ...

`(-5)^(a+2)* (-5)^4=(-5)^5\\\\(-5)^(a+2+4)=(-5)^5\\\\a+6=5 \qquad\text{equating exponents}\\\\a=-1 \qquad\text{subtract 6}`

Here, we used the rule of exponents ...

(a^b)(a^c) = a^(b+c)

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The business of "equating exponents" is equivalent to taking logarithms. In general, the logarithm of a number to a negative base is not defined. However, for the case of integer exponents we have here, there is no problem with doing what we did.

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Check of the answer

(-5)^1 × (-25)^2 = (-5)^5

-5 × 625 = -3125 . . . . true