1. simplify. 5–1(3–2)
a) 45
b) 1/45
c) 15^–3
d) 15^2 
2. simplify. mn^-4/p^0q^-2
a) mq^2/n^4
b) mp/n^4
c) mn^4q^2p^0
d) q^2/mn^4 
3. write in scientific notation. 0.0042
a) 42 × 10^2
b) 4.2 × 10^4
c) 4.2 × 10^3 
d). 42 × 10^4
4. write in standard notation. 6.12 × 10^3
a) 6,120 
b) 612
c) 61,200
d) 61.2
5. simplify. write in scientific notation. 0.5(8 × 10^5)
a) 8 × 5^5
b) 4 × 5^5
c) 8 × 10^5
d) 4 × 10^5 
6. simplify. write in scientific notation. (9 × 10^3)^2
a) 8.1 × 10^5
b) 81 × 10^4
c) 81 × 10^3
d) 8.1 × 10^6 
7. evaluate 1/2a^4b^2 for a = –2 and b = 4.
a) 2 
b) 1/2
c) 3
d) 4
8. is the following statement always, never, or sometimes true?
a number raised to a negative exponent is negative.
a) always
b) never
c) sometimes 
9. simplify (4xy^2)^3(xy)^5 (1 point)
a) 64x^8y^11
b) 64x^15y^30
c) 12x^2y^11
d) 12x^8y^11 
10. simplify (2t^3)^3(0.4r)^2 (1 point)
a) 3.2r^2
b) 1.28r^2/t^-6 
c) 1.28r^2/t^9
d) 0.8r^2/t^-6

1. 5^-1(3^-2) = (1/5)*(1/3^2) = 1/5*3^2 = 1/45

2. mn^-4/p^0q^-2 = m*q^2/n^4  

p^0 = 1

1/q^-2 = q^2

3. 0.0042 = 4.2*10^-3

multiply by 10^-3 is the same as divide by 1000; 4.2 divided by 1000 is 0.0042

4. 6.12 × 10^3 = 6.12*1000 = 6,120

5. 0.5*(8*10^5) = (0.5*8)*10^5 = 4*10^5

6. (9*10^3)^2 = 9^2* (10^3)^2 = 81 * 10^(3*2) = 81*10^6

7. 1/(2a^4) * b^2 for a = –2 and b = 4 = 1/(2*(-2)^4) *4^2 = 1/(2*16) *16 = 1/2

8. Sometimes a number raised to a negative exponent is negative. For example 1^(-2) = 1 and (-1)^(-1) = -1

9. (4xy^2)^3(xy)^5 = 4^3 * x^3 * (y^2)^3 * x^5 * y^5 = 64 * x^(3+5) * y^(2*3) * y^5  = 64*x^8* y^(6+5) = 64*x^8*y^11

10. (2t^(-3))^3 * (0.4r)^2 = 2^3 * t^(-3*3) * (0.4)^2 * r^2 = 8 * t^(-9) * 0.16 * r^2 = 1.28*r^2/t^9

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.