Powers and Roots - Basic - Examples, Exercises and Solutions

Choose the largest value

Let's calculate the numerical value of each of the roots in the given options:

$\sqrt{25}=5\\ \sqrt{16}=4\\ \sqrt{9}=3\\$and it's clear that:

5>4>3>1 Therefore, the correct answer is option A

$\sqrt{25}$

Find the value of n:

$6^n=6\cdot6\cdot6$?

We use the formula: $a\times a=a^2$

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.

$n=3$

What is the answer to the following?

$3^2-3^3$

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:

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

$-18$

Sovle:

$3^2+3^3$

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:

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

36

$\sqrt{441}=$

The root of 441 is 21.

$21\times21=$

$21\times20+21=$

$420+21=441$

$21$

$(\sqrt{380.25}-\frac{1}{2})^2-11=$

According to the order of operations, we'll first solve the expression in parentheses:

$(\sqrt{380.25}-\frac{1}{2})=(19.5-\frac{1}{2})=(19)$

In the next step, we'll solve the exponentiation, and finally subtract:

$(19)^2-11=(19\times19)-11=361-11=350$

350

In the figure in front of you there are 3 squares

Write down the area of the shape in potential notation

Using the formula for the area of a square whose side is b:

$S=b^2$In the picture, we are presented with three squares whose sides from left to right have a length of 6, 3, and 4 respectively:

Therefore the areas are:

$S_1=3^2,\hspace{4pt}S_2=6^2,\hspace{4pt}S_3=4^2$square units respectively,

Consequently the total area of the shape, composed of the three squares, is as follows:

$S_{\text{total}}=S_1+S_2+S_3=3^2+6^2+4^2$square units

To conclude, we recognise through the rules of substitution and addition that the correct answer is answer C.

$6^2+4^2+3^2$

What is the missing exponent?

$-7^{\square}=-49$

2

Choose the expression that is equal to the following:

$2^7$

$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$

Which of the following is equivalent to the expression below?

$$$10,000^1$

$10,000\cdot1$

$\sqrt{49}=$

7

$6^2=$

36

$11^2=$

121

$\sqrt{36}=$

6

$\sqrt{64}=$

8