exponent

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer. Squaring a number means raising it to the power of 2 The square root of a number undoes a square of a number. So square root of x^2 is x x squared is...

total of a number and the square of a number The phrase a number means an arbitrary variable, let's call it x. The square of a number means we raise x to the power of 2. x^2 The total means we add x squared to x: x + x^2

When finding the power of a power, you _____________________ the exponents Multiply Example: (a^b)^c = a^bc

2^46 is how many times as many as 2^42 We can break this apart as follows: 2^46 = 2^42 * 2^4 2^4= 16 times as many

the square of the sum of two numbers Let the first number be x. Let the second number be y. The sum is: x + y Now we square that sum by raising the sum to a power of 2: (x + y)^2

A times r squared multiplied by h r squared means we raise r to the power of 2: r^2 a times r squared: ar^2 Multiplied by h: ahr^2

the total of 3 times the cube of u and the square of u The cube of u means we raise u to the power of 3: u^3 The square of u means we raise u to the power of 2: u^2 The total of both of these is found by adding them together: u^3 + u^2

2/5 the cube of a number The phrase a number means an arbitrary variable, let's call it x. The cube of a number means we raise x to the power of 3: x^3 2/5 of the cube means we multiply x^3 by 2/5: (2x^3)/5

Raise the difference of V and 7 to the 10th The difference of V and 7: V - 7 Raise this to the 10th power: (V - 7)^10

Raise F to the second power then divide G by the result F to the second power: F^2 Divide G by the result: G/F^2

8 is subtracted from the square of x Take this algebraic expression in parts: The square of x means we raise x to the power of 2: x^2 8 subtracted from the square of x is found by subtracting 8 from x^2 x^2 - 8

twice the square of the product of x and y Take this algebraic expression in pieces: The product of x and y means we multiply x and y: xy The square of the product means we raise xy to the power of 2: (xy)^2 = x^2y^2 Twice the square means we multiply the square by 2: 2x^2y^2

3 to the power of 2 times 3 to the power of x equals 3 to the power of 7. Write this out: 3^2 * 3^x = 3^7 When we multiply matching coefficients, we add exponents, so we have: 3^(2 + x) = 3^7 Therefore, 2 + x = 7. To solve this equation for x, we type it into our search engine and we get: x = 5

(2n)^3 without exponents This can be written as follows: 2^3 * n^3 8n^3

Madeline’s science quiz consists of 10 questions, all of which are true or false. How many different choices for answering the 10 questions are possible? 2 ways of answering each True or False Question ^ (10 different ways to answer each question) 2^10 = 1,024 ways

Start with t and cube it. Cubing a variable means raising it to the power of 3: t^3

if 1 person with corona spreads it to 3 people and those people spread it to 3 people, how many people have corona So the spread rate is 3/1 = 3. If 3 people have it, then they spread it to 3 x 3 = 9 people.

1, 9, 25, 49, .......... What is next 1^2 = 1 3^2 = 9 5^2 = 25 7^2 = 49 So this pattern takes odd numbers and squares them. Our next odd number is 9: 9^2 = 81

How can you rewrite the number 1 as 2 to a power? There exists an identity which says, n^0 = 1 where n is a number. So 2^0 = 1

5 times g reduced by the square of h Take this algebraic expression in pieces: 5 times g means we multiply g by 5: 5g The square of h means we raise h to the 2nd power: h^2 5 times g reduced by the square of h means we subtract h^2 from 5g: 5g - h^2