exponent

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

The perfect square less than 30 We know that: 5^2 = 25 6^ = 36 So our answer is 5

(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 -...

Index form of (5^3)^6 Index form is written as a number raised to a power. Let's simplify by multiply the exponents. Since 6*3 = 18, We have: 5^18

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...

5×5 squared Determine index form 5^2 <-- index form Evaluate: 5^2 = 5 * 5 = 25

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)

Raise the sum of k and j to the second power The sum of k and j is written as: k + j Raise the sum to the second power: (k + j)^2

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