Question

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

Answer 1

Answer: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:

Answer 2

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