Make an argument for why (4^2)^4=(4^4)^2

1 answer:

6 0

I hate when it comes to explaining but I gave it my best!

(4^2)^4 is the same as (4^4)^2 because they’re both being squared and multiplied by the a number equaling to the same number, but written differently.

4^2=16 , whereas 4^4=256
HOWEVER
16^4=65536 and 246^2=65536.

Therefore both equal to the same number. It depends on the exponents, and multiplication. If it were to be a different exponent, then they wouldn’t have been the same

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-0.2x^2+0.9x+0.6=y What's the vertex form for this equation?

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Answer: y = -0.2(x - 2.25)² + 1.6125

Step-by-step explanation:

$y = -0.2x^2 + 0.9x + 0.6\\\\y - 0.6 = -0.2x^2 + 0.9x\\\\y - 0.6 =-0.2(x^2-4.5x)\\\\y-0.6+\underline{(-0.2)(2.25)^2}=-0.2(x^2-4.5x+\underline{2.25^2})\\\\y-0.6-1.0125=-0.2(x-2.25)^2\\\\y-1.6125=-0.2(x-2.25)^2\\\\y=-0.2(x-2.25)^2+1.6125$