When
powers to the
same base are
divided, the exponent in the denominator of the fraction is subtracted from the one in the numerator.
multiplied, the exponents are added.
What if the result of the addition or subtraction of exponents is zero?Any base raised to
zero power is
equals 1.
Therefore 100 = 1.
Multiplying powers of ten that have
exponents that are
equal in magnitude but have
opposite signs gives 1.
Dividing powers of ten that have the
same exponent gives 1.
| 10–5 | = 10–5 – ( –5) = 100 = 1 |
| 10–5 |
| 103 × 10–3 = 103–3 = 100 = 1 |
I
n both of the above cases the powers of ten are said to cancel.The inverse of a power of ten is equal to 1 divided by the power of 10 (just like
1/
2 is the inverse of 2).
Using the fact that 1 is equivalent to 10
0, and the division rules above, it can be shown that
the
exponent on the
inverse of a power of 10 has the
same magnitude and the
opposite sign.
| 1 | = 100– 5 = 10– 5 | |
| 105 |
| | (inverse of 105) | |
| 1 | = 100– (–5) = 105 |
| 10– 5 |
| | (inverse of 10–5) |