1. Simplify 5^-1(3^-2)
A. 45
B. 1/45
C. 15^-3
D. 15^2
2. Simplify (3xy^3)^2(xy)^6
A. 9x^8y^12
B. 3x^8y^12
C. 2x^3y^12
D. 9x^8y^9
3. Simplify. Written in scientific notation. 0.5(8 x 10^5)
A. 8 x 5^4
B. 4 x 5^5
C. 8 x 10^5
D. 4 x 10^5
4. Astronomers measure large distances in light-years. One light-year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light-years away from Earth. In scientific notation, approximately how many miles is it?
A. 5.88 x 10^13 miles
B. 5.76 x 10^14 miles
C. 5.88 x 10^12 miles
D. 9.8 x 10^12 miles
5. Simplify. Written in scientific notation. (9 x 10^-3)^2
A. 8.1 x 10^-5
B. 81 x 10^-4
C. 81 x 10^-3
D. 8.1 x 10^-6
6. Evaluate 1/2a^-4b^2 for a= -2 and b= 4.
A. 2
B. 1/2
C. 3
D. 4
7. Is the following statement always, never or sometimes true?
A number raised to a negative exponent is negative.
A. always true
B. never true
C. sometimes true
8. Simplify (4xy^2)^3(xy)^5
A. 64x^8y^11
B. 64x^15y^30
C. 12x^2y^11
D. 12x^8y^11
9. Simplify (2t^-3)^3(0.4r)^2
A. 3.2r^2
B. 1.28r^2 / t^-6
C. 1.28r^2 / t^9
D. 0.8r^2 / t^-6
10. Suppose the growth of a population (in thousands) is represented by the expression 32 x 2.1^x, where x represents the number of years since 2010. Evaluate the expression for the year 2015. Round to the nearest whole number.
A.41
B.1,307
C.67
D. 622
Please Help!!!! I don't understand!!
Here are the answers I got(quiz with practice and reflection, and also for TCAH) Idk if they're all correct since I haven't checked them on symbolab and mathway, but here. I will also add the questions for a complex breakdown and also the answers(by letter) at the end, and just to remember, these answers may or may be wrong, if I made a mistake, please tell me or just write for whatever question I am wrong.
1. 1/45 (did the reciprocal of -5 and -9 into a fraction, and just multiplied both denominators)
2. 9x^8 y^12 rule=(a*b)^n=a^n b^n (9x raised from the power with the ^2, y^6, multiplied with ^3 and ^2, and x^6 y^6= 9x^8 y^12(x2 and x6=x8, and y^6 and y^6=y12, so (9x^8 y^12).
3. 400000/4*x10^5 multiplied 0.5*8*10^5, 0.5*8=(4*x10^5)(400,000)
4. 5.88*10^14 (I just have a guess honestly, I don't really understand this, if someone could explain to me that would be great, I tried subtracting and other such, nothing worked. But yeah)
5. 8.1*10^-5 (should have 81x^2/1000000(6 zeros, ^-6) then turn into originally 81*10^-6, but not there, so just move the decimal from 81 to 8.1, and -6 to -5 and you still would have the same problem)
6. 1/2 (input given a=-2 b=4, so 1/2 -2 ^-4 4^2, -2^4=-16, reciprocal, 1/16, and same with 4^2, 16, so (1/2)*(1/16)*(16=0.5/ 1/2, so (1/2)
7. I think (*sometimes true), although I don't know about this, as 1^-2 would be 1, being positive, and -2^-1 would be -0.5, being not positive, so it could be sometimes true, but please correct me if I am wrong :)
8. 64x^8 y^11 (4xy^2)^3, 3 times 4, x, y=4^3=64, x^3, y^6, so 64x^3y^6, and (xy)^5, x^5, y^5, simplify like terms: x3 and x5, =x8, y6 y5= y11, so we now have (64x^8y^11).
9. 1.28r^2/t^9 (multiply ^3, giving you 2^3, and 3*-3 would be -9, reciprocal into 1/9, and just put in top 2^3/t^9, then (0.4r)^2, same thing, x the raised power of ^2, 0.4^2, r^2, then multiply the fractions, (rule= a*b/c=a*b/c), so, 2^3*0.4^2r^2/t^9, which 2^3=8*0.4=0.16,r^2, 8*.16*r^2=(1.28r^2/t^9).
10. 1,307 (as the question states, it was since 2010(for the population growth), letting x be the year since, and since we are looking for 2015(which is 5 years from 2010, pretty sure y'all now this), we input 5 into x, being now 32*2.1^x, x=5, 32*2.1^5, and so you should have 1,306.9. Since we are supposed to round the nearest whole number(6), 9 is closer to 10, and therefore rounded, would be 1,307.
All Answers(by letter and the actual answer)
1. b(1/45)
2. a(9x^8 y^12)
3. d(4*x10^5)
4. b(5.88*10^14)
5. a(8.1*10^-5)
6. b(1/2)
7. c(*sometimes true)
8. a(64x^8 y^11)
9. c(1.28r^2/t^9)
10. b(1,307)
again, these answers may be wrong, so please be careful and notify me If I am wrong with one of these questions. Also, please be aware that teachers put different questions sometimes, and some quizzes might be outdated, so I advise if you give answers, don't write by letter and instead by the actual answer of the question. Okay goodbye y'all :D
Random student is right
negative powers are reciprocals. So,
5^-1(3^-2) = 1/5^1 * 1/3^2 = 1/5 * 1/9 = 1/45
when powers of like bases are multiplied, add the powers. So,
x^3 * x^2 = x*x*x * x*x = x^5
when powers are raised to powers, multiply them. So,
(x^3)^2 = x^3 * x^3 = x^(3*2) = x^6
Thus,
(3xy^3)^2(xy)^6 = (3^2 x^2 y^6)(x^6 y^6) = 9x^8y^12
scientific notation is just multiplication of coefficients and powers of 10. Follow the usual rules of multiplication and powers shown above.
0.5(8 x 10^5)
= 0.5*8 x 10^5
= 4 x 10^5
The only trick is to make sure that the final coefficient is always less than 10.
For example,
2.5x10^2 * 5.7x10^3 = 14.25x10^(2+3) = 14.25x10^5
But, 14.25 is greater than 10. Since 14.25 = 1.425x10, the final answer is
1.425x10^6
See what you can do with the rest now.