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  1. Simplify. 5–1(3–2)
A45
B1/45
C15^–3
D15^2 ----------------
  1. Simplify. mn^-4/p^0q^-2
Amq^2/n^4
Bmp/n^4
Cmn^4q^2p^0
Dq^2/mn^4 ----------------
  1. Write in scientific notation. 0.0042
A42 × 10^2
B4.2 × 10^4
C4.2 × 10^3 ----------------

D). 42 × 10^4

  1. Write in standard notation. 6.12 × 10^3
A6,120 ----------------
B612
C61,200
D61.2
  1. Simplify. Write in scientific notation. 0.5(8 × 10^5)
A8 × 5^5
B4 × 5^5
C8 × 10^5
D4 × 10^5 ----------------
  1. Simplify. Write in scientific notation. (9 × 10^3)^2
A8.1 × 10^5
B81 × 10^4
C81 × 10^3
D8.1 × 10^6 ----------------
  1. Evaluate 1/2a^4b^2 for a = –2 and b = 4.
A2 ----------------
B1/2
C3
D4
  1. Is the following statement always, never, or sometimes true?

A number raised to a negative exponent is negative.

Aalways
Bnever
Csometimes ----------------
  1. Simplify (4xy^2)^3(xy)^5 (1 point)
A64x^8y^11
B64x^15y^30
C12x^2y^11
D12x^8y^11 ----------------
  1. Simplify (2t^3)^3(0.4r)^2 (1 point)
A3.2r^2
B1.28r^2/t^-6 ----------------
C1.28r^2/t^9
D0.8r^2/t^-6

Verified Answer :

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  \(1.28 r^2 \times t^9\)

1. 5^-1(3^-2) = (1/5)(1/3^2) = 1/53^2 = 1/45

2. mn^-4/p^0q^-2 = mq^2/n^4  

p^0 = 1

1/q^-2 = q^2

3. 0.0042 = 4.210^-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 = 6.121000 = 6,120

5. 0.5(810^5) = (0.58)10^5 = 410^5

6. (910^3)^2 = 9^2 (10^3)^2 = 81 10^(32) = 8110^6

7. 1/(2a^4) b^2 for a = –2 and b = 4 = 1/(2(-2)^4) 4^2 = 1/(216) 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^(23) y^5  = 64x^8 y^(6+5) = 64x^8y^11

10. (2t^(-3))^3 (0.4r)^2 = 2^3 t^(-33) (0.4)^2 r^2 = 8 t^(-9) 0.16 r^2 = 1.28*r^2/t^9

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