MATH SOLVE

2 months ago

Q:
# Exponents and Powers QuestionNeed help, please answer with explanation.

Accepted Solution

A:

Answer: a = -1Step-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)_____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._____Check of the answer(-5)^1 × (-25)^2 = (-5)^5-5 × 625 = -3125 . . . . true