Exponent Rules
The product rule for exponents
Keep the same base and add the exponents together
There were about 18 million teenagers in the United States. They each sent an average of 900 text messages per month. About how many text messages did all of the teenagers in the United States send each month? (Answer must be in Scientific Notation)
2 x 10^3
( 3.5 × 10^−2)( 9 × 10^4)
3.15 × 10^3
9.17 x 10^3
9170
770
7.70 x 10^2
The quotient rule for exponents
Keep the same base and subtract the exponents
The speed of light in cold air is approximately 3 × 10^8 meters/sec. The speed of sound in cold air is approximately 3 × 10^2 meters/sec. The speed of light in cold air is how many times larger than the speed of sound in cold air?
1 x 10^6
(3 × 10^−2) / (8 × 10^-1)
3.75 × 10^−2
2.2517 x 10^3
2251.7
87200
8.72 x 10^4
The power to a power rule
Keep the same base and multiply the exponents together
The population of Mathville is 8.4x10^3. The population of Algeville is 1.3x10^4 . How many more people are there in Algeville?
4.6 x 10^3
(2.5 x 10^1) + (6.14 x 10^4)
6.1425 x 10^4
1.523 x 10^-3
.001523
74171.7
7.41717 x 10^4
The negative exponent rule
Put the entire number over one and flip it, make the exponent positive in the denominator
How many times larger the population of Thailand (6 x 10^8) is than the population of Panama (4 x 10^6).
1.5 x 10^2
(8.14 x 10^5) - (7.8 x 10^2)
8.1322 x 10^5
0.0000573
5.73 x 10^-5
The power of a quotient rule
The exponent gets distributed to the numerator and denominator and simplified.
About 3.8×10^8 people live in Arizona. About 2.1 ×10^7 people live in Kansas. About how many more people live in Arizona than live in Kansas?
3.59 x 10^8
( 8.8 × 10^−5)^-5
1.895 × 10^20
30 x 10^3
0.000000813253
8.13253 x 10^-7