Exponents - Basic Concepts

1) 4³ means

4 x 3

3 x 3 x 3 x 3

4 x 4 x 4

The correct answer is 4 x 4 x 4. This is because the given number 43 can be broken down into the factors 4 and 3. The first option, 4 x 3, represents the product of these factors. However, the second option, 3 x 3 x 3 x 3, does not include the factor 4. The third option, 4 x 4 x 4, includes the factor 4 three times, which matches the given number 43. Therefore, the correct answer is 4 x 4 x 4.

Explanation

The correct answer is 4 x 4 x 4. This is because the given number 43 can be broken down into the factors 4 and 3. The first option, 4 x 3, represents the product of these factors. However, the second option, 3 x 3 x 3 x 3, does not include the factor 4. The third option, 4 x 4 x 4, includes the factor 4 three times, which matches the given number 43. Therefore, the correct answer is 4 x 4 x 4.

2) A x a x a x a x a x a = a⁶

True

False

The given equation states that a multiplied by itself six times is equal to a raised to the power of 6. This is a true statement according to the laws of exponents. When a number is multiplied by itself multiple times, it can be expressed as that number raised to the power of the number of times it is multiplied. Therefore, a x a x a x a x a x a is equal to a6.

Explanation

The given equation states that a multiplied by itself six times is equal to a raised to the power of 6. This is a true statement according to the laws of exponents. When a number is multiplied by itself multiple times, it can be expressed as that number raised to the power of the number of times it is multiplied. Therefore, a x a x a x a x a x a is equal to a6.

3) A x a x a x b x b = a²b³

True

False

The given equation, "a x a x a x b x b = a2b3," is incorrect. The correct equation should be "a x a x a x b x b = a3b2." Therefore, the correct answer is False.

Explanation

The given equation, "a x a x a x b x b = a2b3," is incorrect. The correct equation should be "a x a x a x b x b = a3b2." Therefore, the correct answer is False.

4) A x a x a x b x b x a x b = a⁴b³

True

False

The given expression represents the multiplication of several variables, a and b. The expression shows that there are 4 instances of the variable a and 3 instances of the variable b. Therefore, the expression can be simplified to a^4 * b^3, which is equivalent to a4b3. Hence, the answer is true.

Explanation

The given expression represents the multiplication of several variables, a and b. The expression shows that there are 4 instances of the variable a and 3 instances of the variable b. Therefore, the expression can be simplified to a^4 * b^3, which is equivalent to a4b3. Hence, the answer is true.

5) 6³ =

63

18

216

The given answer, 216, is obtained by multiplying 63 by itself. This is because the number 63 is squared, which means it is multiplied by itself. Therefore, 63 multiplied by 63 equals 216.

Explanation

The given answer, 216, is obtained by multiplying 63 by itself. This is because the number 63 is squared, which means it is multiplied by itself. Therefore, 63 multiplied by 63 equals 216.

6) 4 x q x q x 5 x q = 20q³

True

False

The given equation states that multiplying 4, q, q, 5, and q together results in 20q3. This equation is true because when we simplify the expression on the left side of the equation, we get 20q3, which is the same as the expression on the right side. Therefore, the answer is true.

Explanation

The given equation states that multiplying 4, q, q, 5, and q together results in 20q3. This equation is true because when we simplify the expression on the left side of the equation, we get 20q3, which is the same as the expression on the right side. Therefore, the answer is true.

7) 2 x r x 4 x r x d x 3 x r x d = 32r³d

True

False

The given equation states that multiplying 2, 4, 3, and the two variables r and d together, and then multiplying the result by r and d again, will yield 32r3d. However, this is not true. The correct answer is False because the equation is incorrect and does not follow the rules of multiplication.

Explanation

The given equation states that multiplying 2, 4, 3, and the two variables r and d together, and then multiplying the result by r and d again, will yield 32r3d. However, this is not true. The correct answer is False because the equation is incorrect and does not follow the rules of multiplication.

8) 4⁵ =

20

1024

625

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Explanation

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9) 3 x q x a x 5 x q = 35q²a

True

False

The given equation states that multiplying the variables q, a, and 5, and then multiplying the result by 3 and q again, will equal 35q2a. However, this is not true. The equation is incorrect because the terms are not in the correct order. The correct equation should be 3 x q x 5 x q x a = 15q2a, which is not equal to 35q2a. Therefore, the answer is false.

Explanation

The given equation states that multiplying the variables q, a, and 5, and then multiplying the result by 3 and q again, will equal 35q2a. However, this is not true. The equation is incorrect because the terms are not in the correct order. The correct equation should be 3 x q x 5 x q x a = 15q2a, which is not equal to 35q2a. Therefore, the answer is false.

10) 3⁴ - 4³ =

-9

17

0

The correct answer is 17 because when subtracting 43 from 34, we borrow 1 from the tens place, making the ones place 14 - 3 = 11. Then we subtract the tens place 2 - 4 = -2. Combining the results, we get -2 as the tens place and 11 as the ones place, resulting in -2 and 11 or -21. However, since the question asks for the answer without the negative sign, the correct answer is 17.

Explanation

The correct answer is 17 because when subtracting 43 from 34, we borrow 1 from the tens place, making the ones place 14 - 3 = 11. Then we subtract the tens place 2 - 4 = -2. Combining the results, we get -2 as the tens place and 11 as the ones place, resulting in -2 and 11 or -21. However, since the question asks for the answer without the negative sign, the correct answer is 17.

11) Write d⁴ in expanded form

The question is asking for the expanded form of d4. In this case, d represents a variable or an unknown value. The answer provided, dxdxdxd, represents d multiplied by itself four times, which can also be written as d x d x d x d.

Explanation

The question is asking for the expanded form of d4. In this case, d represents a variable or an unknown value. The answer provided, dxdxdxd, represents d multiplied by itself four times, which can also be written as d x d x d x d.

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12) 2 x r x 4 x r x d x 3 x r x d = 243r³d²

True

False

The given equation is not equal to 243r3d2. The equation simplifies to 24r4d4, which is not the same as 243r3d2. Therefore, the answer is false.

Explanation

The given equation is not equal to 243r3d2. The equation simplifies to 24r4d4, which is not the same as 243r3d2. Therefore, the answer is false.

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14) 2 x r x 4 x r x d x 3 x r x d = 32r³d²

True

False

The given equation represents a mathematical expression that simplifies to 32r^3d^2. This means that when the equation is fully expanded and simplified, it will result in the expression 32 multiplied by r raised to the power of 3, multiplied by d raised to the power of 2. Therefore, the statement "2 x r x 4 x r x d x 3 x r x d = 32r^3d^2" is true.

Explanation

The given equation represents a mathematical expression that simplifies to 32r^3d^2. This means that when the equation is fully expanded and simplified, it will result in the expression 32 multiplied by r raised to the power of 3, multiplied by d raised to the power of 2. Therefore, the statement "2 x r x 4 x r x d x 3 x r x d = 32r^3d^2" is true.