Evaluate:

1. 3^-2                        

2. (-4)^-2                        

3. ( )^-5   

Simplify and express the result in power notation with positive exponent:

1. (-4)⁵ ÷ (-4)⁸              

2. (1 ÷ 2³)²           

3. (-3)⁴ × (5 ÷ 3)⁴       

4. (3^-7 × 3^-10) × 3⁵   

5. 2^-3 × (-7)³       

Find the value of:

1. (3⁰ + 4^-1) × 2²                 

2. (2^-1 × 4^-1) ÷ 2^-2         

3. (1 ÷ 2)^-2 + (1 ÷ 3)^-2 + (1 ÷ 4)^-2   

4. (3^-1 + 4^-1 + 5^-1)⁰           

5. {(-2 ÷ 3)^-2}²

Evaluate:

1. (8^-1 × 5³) ÷ 2^-4                                       

2. (5^-1 × 2^-1) × 6^-1

Find the value of m for which 5^m ÷ 5^-3 = 5⁵

Evaluate:

1. {(1 ÷ 3)^-1 + (1 ÷ 4)^-1}^-1                                         

2. (5 ÷ 8)^-7 × (8 ÷ 5)^-4

Simplify:

1. (25 × t^-4) ÷ (5^-3 × 10 × t^-8)  

(t ≠ 0)        

2. (3^-5 × 10^-5 × 125) ÷ (5^-7 × 6^-5)

Express the following numbers in standard form:

1. 0.0000000000085                  

2. 0.00000000000942                 

3. 6020000000000000

4. 0.00000000837                     

5. 31860000000

Express the following numbers in usual form:

1. 3.02 × 10^-6       

2. 4.5 × 10⁴        

3. 3 × 10^-8      

4. 1.0001 × 10⁹     

5. 5.8 × 10¹²   

6. 3.61492 × 10⁶

Express the number appearing in the following statements in standard form:

1. 1 micron is equal to  m.

2. Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

3.  Size of a bacteria is 0.0000005 m.

4. Size of a plant cell is 0.00001275 m.

5. Thickness if a thick paper is 0.07 mm.

In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm.

What is the total thickness of the stack?