7 times the cube of the sum of x and 8
Take this algebraic expression in 3 parts:
The sum of x and 8 means we add 8 to x: x + 8
The cube of this sum means we raise the sum to the 3rd power: (x + 8)^3
7 times this cubed sum means we multiply (x + 8)^3 by 7:
7(x + 8)^3
(n^2)^3 without exponents
This expression evaluates to:
n^(2 *3)
n^6
To write this without exponents, we expand n times itself 6 times:
n * n * n * n * n * n
A boat costs 14950 and decrease in value by 7% per year how much will the boat be worth after 8 years?
If a boat decreases in value 7% in value, then our new value each year is 100% - 7% = 93%. So we have a B(y) function where B(y) is the value of the boat after y years:
B(y) = 14,950 * (1 -...
One fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
The phrase a number means an arbitrary variable, let's call it x
The square of a number means we raise it to the power of 2. So we have x^2
One-fifth means we have a fraction, where we divide our...
A bunny population is doubling every 2 years. There are currently 45 bunnies. How many will there be in 10 years?
Find the number of doubling periods:
Number of Doubling periods = Time / Doubling period
Number of Doubling periods = 10/2
Number of Doubling periods = 5
Create a function to...
A car is purchased for $19000. After each year, the resale value decreases by 30% . What will the resale value be after 4 years?
Set up a book value function B(t) where t is the number of years after purchase date. If an asset decreases by 30%, we subtract it from the original 100% of the...
4 times of the sum of the cubes of x and y
The cube of x means we raise x to the 3rd power:
x^3
The cube of y means we raise y to the 3rd power:
y^3
The sum of the cubes means we add:
x^3 + y^3
4 times the sum of the cubes:
4(x^3 + y^3)
If a, b, and c are positive integers such that a^b = x and c^b = y, then xy = ?
A) ac^b
B) ac^2b
C) (ac)^b
D) (ac)^2b
E) (ac)^b^2
xy = a^b * c^b
We can use the Power of a Product Rule
a^b * c^b = (ac)^b
Therefore:
xy = (ac)^b - Answer C
Given f = cd^3, f = 450, and d = 10, what is c?
A) 0.5
B) 4.5
C) 15
D) 45
E) 150
Plugging in our numbers, we get:
c(10)^3 = 450
Since 10^3 = 1000, we have:
1000c = 450
Typing this equation into our search engine, we get:
c = 0.45 Answer B
Which of the following is equivalent to 9^3/4?
a) 9^1/3
b) 9 ^ 1/4
c) sqrt(3)
d) 3 * sqrt(3)
Since 9 is 3^2, we have 3^(3*2/4) which is 3^6/4
Since 6/4 is 3/2, we have:
3^(3/2)
Since 3/2 is 1 + 1/2, we have:
3^1*sqrt(3)
3*sqrt(3) or option D.
If 3x - y = 12, what is the value of 8^x/2^y
We know 8 = 2^3
So using a rule of exponents, we have:
(2^3)^x/2^y
2^(3x)/2^y
Using another rule of exponents, we rewrite this fraction as:
2^(3x -y)
We're given 3x - y = 12, so we have:
2^12
p more than the square of q
Take this algebraic expression in parts:
Step 1: Square of q means raise q to the 2nd power:
q^2
Step 2: The phrase more means we add p to q^2
q^2 + p
Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this...
divide 8 by t, raise the result to the 7th power.
We take this algebraic expression in two parts:
1. Divide 8 by t
8/t
2. Raise the result to the 7th power. (This means we use an exponent of 7)
(8/t)^7
the cube of the difference of 5 times x and 4
Take this algebraic expression in pieces:
5 times x:
5x
The difference of 5x and 4 means we subtract 4 from 5x:
5x - 4
We want to cube this difference, which means we raise the difference to the power of 3.
(5x - 4)^3
Raise p to the 9th power, multiply the result by q, then divide what you have by r.
Take this in steps:
Raise p to the 9th power: p^9
Multiply the result by q: qp^9
Divide what you have (the result) by r: qp^9/r
(qp^9)/r