The product rule for exponents states that for two or exponents that share the same base, the products is equal to their shared base to the sum of their exponents. Can anyone help me figure this out?

10⁻⁵ · 10⁴ · 10⁸ = 10⁻⁵⁺⁴⁺⁸ = 10⁷

105 = 10 x 10 x 10 x 10 x 10 = 100,000 (5 zeros)

108 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 (8 zeros)

Notice that the number of zeros in the ordinary decimal expression is exactly equal to the power to which 10 is raised.

If the number is expressed in words, first write it down as an ordinary decimal number and then convert. Thus, "ten million" becomes 10,000,000. There are seven zeros, so in powers of ten notation ten million is written 107.

A number which is some power of 1/10 can also be expressed easily in scientific notation. By definition,

1/10 = 10-1 ("ten to the minus one power")

More generally, the expression "10-n" (where n is a whole number) means ( 1/10 )n. Thus

10-3 = ( 1 / 10 )3 = 1 / ( 10 x 10 x 10) = 1/1000

10-8 = ( 1 / 10 )8 = 1/100,000,000

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents

Step-by-step explanation:

We have different information and we need to make a table of that, so

causeRelative Frequency

Pilot Error613

Othe human error75

Weather470

Mechanical Problems311

Sabotage342

Total: 1811

To calculate the relative distribution we need basically divide by the total and multiply for 100.

causeRelative Frequency

Pilot Error613/1811*100 =33.84%

Othe human error75/1811*100 = 4.1%

Weather470/1811*100 = 25.95%

Mechanical Problems311/1811*100 = 17.17%

Sabotage342/1811*100 = 18.88%

Total: 100%

So the relative frequency distribution is,

causeRelative Frequency

Pilot Error33.84%

Othe human error4.1%

Weather25.95%

Mechanical Problems17.17%

Sabotage18.88%

Total: 100%

The vast majority of failures are made by pilots. The best thing to do is offer them more training. Many of these problems are due to ignorance of the terrain or carelessness due to the standardized level of security that flights generally have. Lack of practice in extreme situations can cause these problems.