Find the next term of the series. question. 21,31,22,74?

1st rule:

21,31,22,74 => 12, 13, 22, 47

12 + 1^2 = 13

13 + 3^2 = 22

22 + 5^2 = 47

47 + 7^2 = 96

96 => 69

=> next number after 74 is 69

2nd rule:

21, 31, 22, 74

21 + 31 + 22 = 74

31 + 22 + 74 = 127

=> next number after 74 might also be 127

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!