C5 Order of Operations and Checking Answers

Question 1

how do you simplify the expression -2⁴ versus (-2)⁴

Answer 1

-2⁴ = -16 because the order of operations says first raise to the fourth power and then apply the negative sign (Powers are 1st step, subtraction is the last step.

(-2)⁴ = 16 because the entire expression in parnetheses is raised to the fourth power, equivilant of multiply -2 by itself four times.

Question 2

steps to checking your answers

Answer 2

1. Write out the equation or the problem
2. Insert the answer into the equation (replace the variable)
3. Perform the operations and see if the answer is correct

Question 3

a + a + a + a = 4a because multiplication is just?

Answer 3

repeated addition

Question 4

when adding or subtracting terms that have exactly the same variables you do what?

Answer 4

combine the coefficients

2a + 4a + 5a = 11a

Question 5

adding and subtracting powers what is the rule

Answer 5

in order to add or subtract a term with the same variable, the exponents of the variable must be the same.

x + x + x = 3x

x² + x + x = 2x + x²

Question 6

multiplying and dividing variables is easier than adding and subtracting them, much like fractions because?

Answer 6

you don’t have to find the common denominators

2 * a * a * a * b * b * c = 2a³b²c

Question 7

when multiplying factors containing variables?

Answer 7

multiply the coefficients and variables as usual, if the bases are the same you can multiply the variables by adding their exponents

a x a x b x c = a²bc

Question 8

when dividing variables why do you write the problem as a fraction and use the GCF to divide and reduce?

Answer 8

because unlike multiplication you can divide whole numbers, such as 27/5 which results in a number that is not whole but leaves you with a remainder

Question 9

rules for dividing terms with variables

Answer 9

1. write the problem as a fraction if it isn’t already
2. find the GCF and reduce the coefficients to their lowest terms

(this is the division operation but it doesn’t result in a remainder)

3. subtract the variables (and exponents) each variable is considered seperately

Question 10

simplify expressions with multiplication, addition and subtraction: what are the three steps?

Answer 10

1. Rearrange the factors in each term so you can multiply the variables together seperately. 3m²(2mn) = 3 x 2m²mn
2. Multiply the numbers and add the exponents of the variables that are alike. 3 x 2m²mn = 6m²⁺¹n
3. Combine terms that alike.

Question 11

simply expressions with division, addition and subtraction: what are the three steps?

Answer 11

1. Divide by subtracting the exponents of the common bases: 4x²y³/2xy = 2x^2-1y^3-1
2. Complete subtraction of the exponents: 2x^2-1y^3-1 = 2xy²
3. Add or subtract the terms that are exactly alike–numbers that have the same variables and exponents in common