Exponents Worksheets For Grade 6
This is an exponents worksheet for 6th-grade students. Its primary purpose is to make math easier and more understandable for kids. In this, kids learn about exponents and types of exponents. An exponent is a mathematical term that tells how a base number is multiplied by itself and how we can represent that number. Below, we have various exercises that will help kids understand the concept of an exponent and make math easier. So, we hope that this worksheet will help the kids in problem-solving.
Contents
Exponents Worksheets For 6th Grade Students
Read More: Percent to Fraction Math Worksheet for Grade 6
Exponents With Whole Number Bases Worksheet For Grade 6
1. 82 = 64
2. 91 = 9
3. 17 = 1
4. 53 = 125
5. 94 = 6,561
6. 39 = 19,683
7. 44 = 256
8. 35 = 243
9. 102 = 100
10. 48 = 65,536
In this exercise, kids need to solve the whole number exponent. It is a simple multiplication, which helps kids in their mathematical calculation and teaches how long multiplication like 5x5x5 can be written as 5^3. So in this exercise, there are a total of ten quarries that need to be solved. We have to follow some rules. First, we have to look at the power of a number, and as per the power, we have to multiply the number. Let’s take an example: 8^2. As we can see, the power of 8 is 2. So we have to calculate 8 by two times. And the final answer will be – 8 x 8 = 64.
Exponents With Whole Numbers, Decimals, And Fractional Bases Worksheet For Grade 6
1. 93 = 9 x 9 x 9 = 729
2. 222 = 22 x 22 = 484
3. 303 = 30 x 30 x 30 = 27,000
4. 75 = 7 x 7 x 7 x 7 x 7 = 16,807 5.
5. 15 = 1 x 1 x 1 x 1 x 1 = 1 6.
6. 601 = 60 7.
7. 152 = 15 x 15 = 225
8. 114 = 11 x 11 x 11 x 11 = 14,641
In this exercise, the numbers are a little bit higher, but there is no need to worry about it; if we know the process, we can solve any range of numbers. Above, there are a total of eight questions that we have to solve, and doing this will help kids improve their math skills and make them sharp. To solve this exercise, kids can see the above-solved example; the process will be the same, so we hope kids can perform on their own.
Negative And Zero Exponents Worksheet For Grade 6
1. 6-3 = 1/216
2. 4-5 = 1/1,024
3. 50 = 1
4. 8-1 = 1/8
5. 9-3 = 1/729
6. 0-2 = 1/#
7. 3-4 = 1/81
8. 2-6 = 1/64
Good job! Kids, we hope you have solved the above exercise and now you are ready to learn our new concept of the exponent. In this exercise, kids will see negative and zero exponents and they will learn how to solve this type of exercise. Above, we have a total of eight quarries that need to be solved. To solve this, we have to follow some rules. The first one is to turn the base into a fraction like (6^-3). So we have to turn 6 into a fraction (1/6) and now multiply numbers as per their power. For better understanding, let’s take an example: 6^-3. As per the rule 1/6x6x6. And the final answer will be 1/216. Remember for zero we will get the same answer like 0x0 = 0.
Negative And Zero Exponents With Whole Numbers, Decimals, And Fractional Bases Worksheet For Grade 6
1. (6/7) -2 = 49/36
2. (1/5)-6 = 15625
3. (3/4)-1 = 4/3
4. (7/8)0 = 1
5. (1/2)-7 = 128
6. (6/3)-3 = 1/8
7. (4/9)-4 = 6,561/256
8. (2/5)-5 = 3,125/32
In this exercise, we have the same negative and zero exponent with different patterns. Now the numbers are in reaction form, but you don’t need to worry about it; it is as simple as above. To solve this, we have to apply a formula, which is (a/b)^-n will be (b/a)^n. Let’s simplify this rule: if we are seeing fraction patterns, we only need to change their positions. like in formula a/b changed in b/a, and their power will be positive. For example: (6/7)^-2, as per the formula (7/6)^2. Now calculate as per their power (7×7/6×6). So the final answer will be 49/36.
Exponents Worksheet For Grade 6
1. 2.75 x 2.75 x 2.75 x 2.75 x 2.75 = 2.755
2. 2/4 x 2/4 x 2/4 x 2/4 x 2/4 = (1/2)5
3. -17 x -17 x -17 x -17 x -17 x -17 x -17 = -177
4. 5.4 x 5.4 x 5.4 x 5.4 x 5.4 = 5.45
5. 22 x 22 x 22 x 22 x 22 x 22 = 226
6. 5 x 5 x 5 x 5 x 5 x 5 x 5 = 57
7. -0.9 x -0.9 x -0.9 x -0.9 = -0.94
8. (-6/3) x (-6/3) x (-6/3) = (-6/3)3
This exercise is simple and short; in this kids need to write the power of the given expressions. Above we have a total of eight queries, and for each, we need to write in the form of exponents. To solve this, we have to check how many times the numbers are multiplying, like if a number is multiplying by 3 times (3x3x3), so the exponent will be 3^3. Let’s take an example: 2.75 x 2.75 x 2.75 x 2.75 x 2.75. As we can see, 2.75 is multiplied by five times, so the exponent will be 2.75^5.
Equations With Exponents Worksheet For Grade 6
1. 134 + 182 = 28561 + 324 = 28,885
2. 38 x 45 = 6,561 × 1,024 = 6,726,144
3. 213 – 28 = 8192 – 256 = 7,936
4. 034 x 76 = 0 x 117,649 = 0
5. 314 – 283 = 923,521 – 21,952 = 901,569
6. 106 / 101 = 1000000 / 10 = 100000
7. 47 – 153 = 16384 – 1 = 16383
8. 215 + 560 = 32768 + 1 = 32,769
In this exercise, kids need to perform arithmetic operations with exponents. It is simple and short and helps kids improve their problem-solving skills and learn new concepts. We believe kids have understood our exponent concept and they will perform this exercise on their own and without any help. We have different exponent worksheets on our official page; kids can visit and find new challenging worksheets based on exponents.
Equations With Exponents With Negative Bases Worksheet For Grade 6
1. 212 + (-11)4 = 4,096 + 14,641 = 18,737
2. (-1)20 x 75 = 1 × 16,807 = 16,807
3. (-14)3 – 102 = (−2,744) − 100 = −2,844
4. 60 / (-3)7 = 1 / (−2187) = 1 / (−2187)
5. (-5)6 – 39 = 15,625 − 19,683 = −4,058
6. 071 / 691 = 0 / 69 = 0
7. 831 x 511 = 1 x 4,886,325 = 4,886,325
8. 197 + (-2)21 = 1 x 4,886,325 = 4,886,325
In this exercise, we have to perform the same arithmetic operations with exponents, but with a little bit of a difference. Now the pattern has changed; we have negative exponents in the bracket. Don’t worry, we need to remember that when we are calculating negative exponents in a bracket, their sign gets changed. Like negative will be positive. Let’s solve a query: 212 + (-11)^4. First, let’s solve 2^12. So we have to multiply 2 by itself 12 times and the result will be 4,096. Now let’s solve the negative exponent (-11)^4, as per the above definition, the negative will convert into positive, so 11^4. Now we have to multiply 11 by itself four times and we will get 14,641. So the final answer will be 4,096 + 14,641 = 18,737.
Equations With Exponents With Decimal And Fractional Bases Worksheet For Grade 6
1. 0.33 x 65 = 0.027 x 7,776 = 210.432
2. 87 + 083 = 2,097,152 + 0 = 2,097,152
3. 44 / (3/4)3 = 256 / 64/27 = 16,384 / 27
4. 310 / 199 = 59,049 + 1 = 59,050
5. (10/5)2 x (4/8)6 = 4 x 1/64 = 1/16
6. 55 x (1/25)2 = 3,125 / 625 = 5
7. 2.42 – 0.71 = 5.76 − 0.7 = 5.06
8. 96 – 5.03 = 531,441 − 125 = 531,316
Good job! Kids, we are very glad that you are here to solve this exercise and believe that you have solved all the exercises above. In this exercise, we have to perform arithmetic operations with decimal numbers. It is simple and helpful for kids; they will learn how decimal exponents will be solved. Solving this exercise will help kids to handle complex math problems and improve their logical thinking. We know that kids have understood our concept and they will solve this exercise without any help.
Congratulation! Kids, for solving all the exercises. It is a very happy moment for us to know that our kids have solved all the exercises. Believe us, this concept will boost your confidence and encourage you to handle more complex mathematical concepts. We want kids to practice this type of concept daily, which makes their logical thinking strong and prepares them for future grades. If kids like our concept and want to solve more concepts like this, we have different exponent worksheets for grades 5th to 6th available on our page. We would be happy for you to solve more of our worksheets.
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