Question

1. Simplify. 5–1(3–2)

Answer 1

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

Answer 2

Answer with explanation:

Using following law of indices

$1.x^a \times x^b=x^{a+b}\\\\2. (x^m)^n=x^{mn}\\\\ 3. x^{-n}=\frac{1}{x^n}\\\\4. \frac{x^m}{x^n}=x^{m-n}$

$1.5^{-1}\times 3^{-2}=\frac{1}{5}\times\frac{1}{3^2}\\\\=\frac{1}{5\times9}\\\\=\frac{1}{45}\\\\2. \frac{mn^{-4}}{p^0*q^{-2}}=\frac{mq^2}{n^4}\\\\ 3.0.0042=4.2\times 10^3\\\\4.6.12 \times 10^3=6.12 \times 1000=6120\\\\ 5.0.5 \times(8\times10^5})=\frac{1}{2}\times8 \times 10^5=4\times 10^5\\\\6. (9 \times 10^3)^2=9^2 \times (10^3)^2=81 \times 10^6\\\\7.( \frac{1}{2}a^{-4}\times b^2 )_{a=-2,b=4}{\text{or}}( \frac{1}{2}a^{4}\times b^{-2} )_{a=-2,b=4}=\frac{1}{2}\times (-2)^{-4}\times(4)^2{\text{or}}=\frac{1}{2}\times (-2)^{4}\times(4)^{-2}=\frac{16}{2\times16}=\frac{1}{2}$

$9. (4\times x\times y^2)^3\times (xy)^5=4^3\times x^3\times (y^2)^3\times x^5 \times y^5\\\\=64\times x^{3+5}\times y^{5+6}\\\\=64x^8y^{11}\\\\10.(2\times t^3)^3(0.4\times r)^2=2^3 \times (t^3)^3\times (0.4)^2 \times r^2=8\times t^9 \times 0.16 \times r^2=1.28r^2t^9$

8. A number raised to a negative exponent is negative.

Explaining with the help of few examples

 $1.2^{-3}=\frac{1}{2^3}=\frac{1}{8}\\\\ 2.(-3)^{-3}=\frac{1}{(-3)^{3}}=\frac{-1}{27}$

Option C: Sometimes

1.Option B

2.Option A

3.Option C

4.Option A

5.Option D

6.  $81 \times 10^6$

7.Option B

8.Option C

9.Option A

10.Option  $1.28 r^2 \times t^9$