Powers: Solving the equation

Power greater than squarePower of a fractionUsing additional geometric shapesUsing areaComplete the missing numbersComplete the missing numberSimple exerciseIdentify the greater valueSolving the problem
Question 1

Find the value of n:

\( 6^n=6\cdot6\cdot6 \)?

Question 2

What is the answer to the following?

\( 3^2-3^3 \)

Question 3

Sovle:

\( 3^2+3^3 \)

Examples with solutions for Powers: Solving the equation

Exercise #1

Find the value of n:

6n=6⋅6⋅6 6^n=6\cdot6\cdot6 ?

Video Solution

Step-by-Step Solution

We use the formula: a×a=a2 a\times a=a^2

In the formula, we see that the power shows the number of terms that are multiplied, that is, two times

Since in the exercise we multiply 6 three times, it means that we have 3 terms.

Therefore, the power, which is n in this case, will be 3.

Answer

n=3 n=3

Exercise #2

What is the answer to the following?

32−33 3^2-3^3

Video Solution

Step-by-Step Solution

Remember that according to the order of operations, exponents come before multiplication and division, which come before addition and subtraction (and parentheses always before everything),

So first calculate the values of the terms in the power and then subtract between the results:

32−33=9−27=−18 3^2-3^3 =9-27=-18 Therefore, the correct answer is option A.

Answer

−18 -18

Exercise #3

Sovle:

32+33 3^2+3^3

Video Solution

Step-by-Step Solution

Remember that according to the order of operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms in the power and then subtract between the results:

32+33=9+27=36 3^2+3^3 =9+27=36 Therefore, the correct answer is option B.

Answer

36