Vocabulary
What is the definition of a rational exponent?
A rational exponent is an exponent that is a fraction, where the numerator is the power to which the base is raised, and the denominator is the root of the base.
Translate the following word problem into a mathematical expression: 'The area of a square is 253/2 square units.'
253/2
State the product rule for exponents.
The product rule states that am x an = am+n
What is the property of exponents that states a0=1
The zero exponent rule
If a square has side length 41/2 meters, what is the area of the square?
The area of the square is 8 square meters.
Explain the difference between an integer exponent and a rational exponent.
An integer exponent is a whole number exponent, while a rational exponent is a fraction exponent.
A bacteria population triples every 6 hours. If the initial population is 100, what will be the population after 18 hours?
The population after 18 hours is 800 bacteria.
Simplify the expression (23)-2.
(23)-2 = 2-6 = 1/26 = 1/64
Explain why 0.51/2 equals 0.5 squared.
0.51/2 equals 0.5 squared because both represent the square root of 0.5.
What is the annual interest rate if $1000 grows to $1210 in 2 years with continuous compounding?
The annual interest rate is approximately 10.5%.
Give an example of a rational exponent expression.
Any expression is fine.
If a car depreciates by 10% each year, how much will a car worth $20,000 be worth after 5 years?
The car will be worth $11,809.80 after 5 years.
Using the quotient rule, simplify the expression 54/52 .
54/52 = 54-2 = 52 = 25
State the property of exponents that allows you to combine the bases when raising a power to a power.
The power of a power rule.
If a sound decreases by 6 decibels every 3 meters, how much will it decrease after traveling 12 meters?
The sound will decrease by 24 decibels after traveling 12 meters.