Introduction of Distributive Property Exponents:
Exponent is said to be the number to the power. Example: Am, here the number A is the base number and the power of the number A is m which is called exponent.
Here we see about the distributive Properties of Exponents.
The general form of the distributive Properties of Exponents:
(AB)m = Am Bm
Proof - Distributive Property Exponents:
Let take the example of (PQ)2
To prove (PQ)2 = P2 * Q2
(PQ)2 = PQ * PQ
= P * Q * P * Q
= P * P * Q * Q
= P2 * Q2
We proved the distributive property exponents.
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Example Problem - Distributive Property Exponents:
Case 1: Base - Number and Exponent - Integer:
Example 1:
What is the value of the expression (2242)2?
Solution:
(2242)2 = 22 * 2 42 * 2
= 24 44
Answer: (2242)2 = 24 44
Case 2: Base – Variable and Exponents – Integer:
Example 2:
What is the value of the expression (A2B3)2?
Solution:
(A2B3)2 = A2 * 2 B3 * 2
= A4 B6
Answer: (A2B3)2 = A4 B6
Case 3: Base – Variable and Exponents – Negative and Positive fraction:
Example 3:
What is the value of the expression `(A^(3/2) . B ^ (-1/4))^2` ?
Solution:
`(A^(3/2) . B ^ (-1/4))^2`= `A^(3/2 * 2) . B ^ (-1/4 * 2)`
= `A^(3) . B ^ (-1/2)`
Answer: `(A^(3/2) . B ^ (-1/4))^2` = `A^(3) . B ^ (-1/2)`
Case 4: Base – Variable and Exponents – Positive decimals:
Example 4:
What is the value of the expression (A0.5 B1.3)3?
Solution:
(A0.5B1.3)3 = A0.5 * 3 B1.3 * 3
= A1.5 B3.9
Answer: (A0.5B1.3)3 = A1.5 B3.9
Case 5: Base – Variable expressed in fraction and Exponents – Integer
Example 5:
What is the value of the expression `((A^2)/(B^3))^2` ?
Solution:
`((A^2)/(B^3))^2` = `A^(2 * 2)/(B^(3 * 2))`
= `A^(4)/(B^(6))`
Answer: `((A^2)/(B^3))^2`= `A^(4)/(B^(6))`
Case 6: Using Exponent – zero
Example 6:
What is the value of the expression (A0B)2?
Solution:
(A0B)2 = A0 * 2 B1 * 2
= A0 B2
= 1 * B2 = B2
Answer: (A0B)2 = B2
Practice Problem - Distributive Property Exponents:
Problem 1:
What is the value of the expression (X2 A)2?
Answer: X4A2
Problem 2:
What is the value of the expression (P0Q2)1/2?
Answer: Q
Exponent is said to be the number to the power. Example: Am, here the number A is the base number and the power of the number A is m which is called exponent.
Here we see about the distributive Properties of Exponents.
The general form of the distributive Properties of Exponents:
(AB)m = Am Bm
Proof - Distributive Property Exponents:
Let take the example of (PQ)2
To prove (PQ)2 = P2 * Q2
(PQ)2 = PQ * PQ
= P * Q * P * Q
= P * P * Q * Q
= P2 * Q2
We proved the distributive property exponents.
Stuck on any of these topics calculus word problem solver, online free math help try out some best math website like mathsisfun, mathcaptain.com and math dot com.
Example Problem - Distributive Property Exponents:
Case 1: Base - Number and Exponent - Integer:
Example 1:
What is the value of the expression (2242)2?
Solution:
(2242)2 = 22 * 2 42 * 2
= 24 44
Answer: (2242)2 = 24 44
Case 2: Base – Variable and Exponents – Integer:
Example 2:
What is the value of the expression (A2B3)2?
Solution:
(A2B3)2 = A2 * 2 B3 * 2
= A4 B6
Answer: (A2B3)2 = A4 B6
Case 3: Base – Variable and Exponents – Negative and Positive fraction:
Example 3:
What is the value of the expression `(A^(3/2) . B ^ (-1/4))^2` ?
Solution:
`(A^(3/2) . B ^ (-1/4))^2`= `A^(3/2 * 2) . B ^ (-1/4 * 2)`
= `A^(3) . B ^ (-1/2)`
Answer: `(A^(3/2) . B ^ (-1/4))^2` = `A^(3) . B ^ (-1/2)`
Case 4: Base – Variable and Exponents – Positive decimals:
Example 4:
What is the value of the expression (A0.5 B1.3)3?
Solution:
(A0.5B1.3)3 = A0.5 * 3 B1.3 * 3
= A1.5 B3.9
Answer: (A0.5B1.3)3 = A1.5 B3.9
Case 5: Base – Variable expressed in fraction and Exponents – Integer
Example 5:
What is the value of the expression `((A^2)/(B^3))^2` ?
Solution:
`((A^2)/(B^3))^2` = `A^(2 * 2)/(B^(3 * 2))`
= `A^(4)/(B^(6))`
Answer: `((A^2)/(B^3))^2`= `A^(4)/(B^(6))`
Case 6: Using Exponent – zero
Example 6:
What is the value of the expression (A0B)2?
Solution:
(A0B)2 = A0 * 2 B1 * 2
= A0 B2
= 1 * B2 = B2
Answer: (A0B)2 = B2
Practice Problem - Distributive Property Exponents:
Problem 1:
What is the value of the expression (X2 A)2?
Answer: X4A2
Problem 2:
What is the value of the expression (P0Q2)1/2?
Answer: Q
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