Evaluate the following expressions A 42 x 102 42 x 105 B 25

Evaluate the following expressions.

A. (4.2 x 10²) (4.2 x 10⁵)       B. (2.5 x 10^-2)⁴         C. 9.6 x 10² over 3.2 x 10⁵

Part 1: Write your answer in scientific notation.

Part 2: Write these 3 answers (A, B, C) in standard form.

Solution

A)

1)

(4.2 x 10²) (4.2 x 10⁵)   

we muliply the number i.e. 4.2 and for the multiplication of 10² and 10⁵ , we can see that the base are same \"10\" so we add the exponents.

we get

17.64 X 10²⁺⁵                  // the exponents gets added and 4.2*4.2 = 17.64

17.64 x 10⁷

or 1.764 x 10⁸                         // here we moved the decimal point by 1 digit so we add \"1\" to thhe expoent of \"10\"

1.764 x 10⁸

B)

(2.5 x 10^-2)⁴   

                                              //       (a^b)^c   = a^b*c the exponents gets multiplied

we get

2.5⁴ x 10^(-2)*4

39.0625 x 10^-8                                   // positive number *negative number = egative number

now we shift the decimal point by 1 point towardsleft hand side so we add \'1\" to the exponent of \"10\"

3.90625 x 10^-7

C)

9.6 x 10² / 3.2 x 10⁵

we divide the number bedore \"multiplication symbol \" as usual and subtract the exponent \"exponent of numerator - exponent of denominator\"

3 x 10^2-5                            // 9.6 / 3.2 = 3           and x^a/x^b = x^a-b

3 x 10^-3

2)

A)

1.764 x 10⁸

since the exponent of 10 is positive number

we move the decimal point to the right hand side by the value of exponent of 10 i.e. 8

we get

176400000

B)

3.90625 x 10^-7

since the exponent of 10 is negative so we move the decimal point towards left hand side

so we move the decimal point 7 places towards left

0.000000390625

C)

3 x 10^-3

here the exponent of 10 is a negative number so we move the decimal point towards left hand side by 3 places

we can write 3 x 10^-3 as

3.0 x 10^-3

now we move the decimal point

0.003