Answer:
a = -1
Step-by-step 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 ...
[tex](-5)^{a+2}\times (-5)^4=(-5)^5\\\\(-5)^{a+2+4}=(-5)^5\\\\a+6=5 \qquad\text{equating exponents}\\\\a=-1 \qquad\text{subtract 6}[/tex]
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
