Rule of Exponent in Squaring Numbers and/or Square Root
In multiplication of two variables having a second degree or greater, the exponents of the base will be added. It is only applicable if the base of two terms are the same. Squaring or term is similar to a term multiplying by itself. You can multiply the exponents in two, since they are congruent (having the same base and exponent). For example,
(a²)² → (a²)(a²) = a, exponent = 2 + 2 = 4
(a²)(a²) = a⁴
Product Rule of Exponent
The product rule in exponent, in order to multiply two terms in easiest way, it states that product of two or more terms with the same base is equal to the base raised to the sum of all the exponents.
Formula
(a^x) + (a^y) = a^(x+y)
Example
(x²)² = x⁴
(x²y²)² = x⁴y⁴
(x³)(x⁴) = x⁷
(x³)(x²)(x) = x⁶
Given Question
Why do we divide the exponents by two when obtaining the square root of x^4y^6?
Answer and Explanation
The equation x⁴y⁶ is the square terms of x²y³. In squaring terms, the exponent was double, thus in order to get the square root of the terms, just divide by two. Remember, square of a number and/or terms is the value that when it was multiplied by itself. As cited above, apply the rules of exponent specifically in product rule.
How to Find the Square Root of the Term
Identify the base and exponent.
You must identify the base and exponent, and group all the terms. Example, x⁴y² → (x⁴)(y²).
For complex terms, you must simplify the term first, by separating variables and constant.
Get the exponents of each term and divide by two. Example, x⁴ →4 ÷ 2 = 2, and y² →2 ÷ 2 = 1
Copy the base, and simplify.
Summary
Why do you need to divide the exponent of the base of the terms in getting the square root? Because square root of a number is the value when multiplied by itself. The concept of multiplying a number or term by itself is similar to the rules of multiplying two or more terms. You need to apply the product rule of the exponent, which is product of two or more terms with the same base is equal to the base raised to the sum of all the exponents. Multiplying terms by it self has the same value of exponent, thus it is simply as multiplying by two.
Answers & Comments
Verified answer
Rule of Exponent in Squaring Numbers and/or Square Root
In multiplication of two variables having a second degree or greater, the exponents of the base will be added. It is only applicable if the base of two terms are the same. Squaring or term is similar to a term multiplying by itself. You can multiply the exponents in two, since they are congruent (having the same base and exponent). For example,
(a²)² → (a²)(a²) = a, exponent = 2 + 2 = 4
(a²)(a²) = a⁴
Product Rule of Exponent
The product rule in exponent, in order to multiply two terms in easiest way, it states that product of two or more terms with the same base is equal to the base raised to the sum of all the exponents.
Formula
(a^x) + (a^y) = a^(x+y)
Example
(x²)² = x⁴
(x²y²)² = x⁴y⁴
(x³)(x⁴) = x⁷
(x³)(x²)(x) = x⁶
Given Question
Why do we divide the exponents by two when obtaining the square root of x^4y^6?
Answer and Explanation
The equation x⁴y⁶ is the square terms of x²y³. In squaring terms, the exponent was double, thus in order to get the square root of the terms, just divide by two. Remember, square of a number and/or terms is the value that when it was multiplied by itself. As cited above, apply the rules of exponent specifically in product rule.
How to Find the Square Root of the Term
Summary
Why do you need to divide the exponent of the base of the terms in getting the square root? Because square root of a number is the value when multiplied by itself. The concept of multiplying a number or term by itself is similar to the rules of multiplying two or more terms. You need to apply the product rule of the exponent, which is product of two or more terms with the same base is equal to the base raised to the sum of all the exponents. Multiplying terms by it self has the same value of exponent, thus it is simply as multiplying by two.
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