I just got this worksheet from school for my Algebra II class. It is about patterns in exponents. I have so far:
4^4=256
4^3=64
4^2=16
4^1=4
4^0=1
4^-1=1/4
4^-2=1/16
4^-3=1/64
3^4=81
3^3=27
3^2=9
3^1=3
3^0=1
3^-1=1/3
3^-2=1/9
3^-3=1/27
2^4=16
2^3=8
2^2=4
2^1=2
2^0=1
2^-1=1/2
2^-2=1/4
2^-3=1/8
I also figured out some patterns, like 4^4(256)/4^3(64)=4 and that anything to the first power is still the base, and that the negatives are like the positives but on the numerator there is one. My worksheet wants me to explain why x^0=1, but I don't understand that at all. I looked on the website and everything, but it still didn't make sense to me. My worksheet also wants me to explain why x^-1=1/x and why x^-2=1/x^2. My worksheet then goes on to have me simplify 1/(1/3) and 2/(3/5) and to show my work, and then 1 / x^-1 and 1 / x^-2 and to show my work again. The last thing on my worksheets says, "Based on your observations, what will 5/x^-1 equal? What will 6/x^-3 equal? What will 10/(2x^-4) equal?" That's it!
Please and thank you for my help!!! For me, this is due in two days, but I won't have a ton of time during these days to work on it, so I'd like to finish it today.
4^4=256
4^3=64
4^2=16
4^1=4
4^0=1
4^-1=1/4
4^-2=1/16
4^-3=1/64
3^4=81
3^3=27
3^2=9
3^1=3
3^0=1
3^-1=1/3
3^-2=1/9
3^-3=1/27
2^4=16
2^3=8
2^2=4
2^1=2
2^0=1
2^-1=1/2
2^-2=1/4
2^-3=1/8
I also figured out some patterns, like 4^4(256)/4^3(64)=4 and that anything to the first power is still the base, and that the negatives are like the positives but on the numerator there is one. My worksheet wants me to explain why x^0=1, but I don't understand that at all. I looked on the website and everything, but it still didn't make sense to me. My worksheet also wants me to explain why x^-1=1/x and why x^-2=1/x^2. My worksheet then goes on to have me simplify 1/(1/3) and 2/(3/5) and to show my work, and then 1 / x^-1 and 1 / x^-2 and to show my work again. The last thing on my worksheets says, "Based on your observations, what will 5/x^-1 equal? What will 6/x^-3 equal? What will 10/(2x^-4) equal?" That's it!
Please and thank you for my help!!! For me, this is due in two days, but I won't have a ton of time during these days to work on it, so I'd like to finish it today.
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