Solution: Show Basically, we will solve this question by the multiplication rule of exponents and power. The exponent of any number represents how many times to use the number in a multiplication. We have given that, x to the power of 1/2 Basically, the rules for exponentiation states that, if n is a positive integer and x is any real number, then an can be represented as: an = a × a × … × a (n times) Hence x to the power of 1/2 can be written as x(1/2) which is a fractional exponent. Where the number x is called the base, whereas (1/2) is the power or exponent of the expression. Any exponent of (1/2) is actually the square root of that number. Therefore, x(1/2) = √x Hence, x to the power of 1/2 can be written as √x. What is the value of x to the power of 1/2?Summary: x to the power of 1/2 is √x. By using the multiplication rule of exponents and power we will solve this question. The exponent of any number represents how many times to use the number in a multiplication. Answer: 2 to the power of 1/2 is √2 or 1.4142…Let's solve this question step by step. Explanation: Given that, 2 to the power of 1/2 Basically, the rules for exponentiation states that If n is a positive integer and x is any real number, then an can be represented as: an = a × a × … × a (n times) Hence 2 to the power of 1/2 can be written as 2(1/2) which is a fractional exponent. Where the number 2 is called the base, whereas (1/2) is the power or exponent of the expression. Any exponent of (1/2) is actually the square root of that number. Therefore, 2(1/2) = √2 or 1.4142… Hence, 2 to the power of 1/2 is √2 or 1.4142…Created by Mateusz Mucha and Piotr Małek Reviewed by Bogna Szyk and Jack Bowater Last updated: Mar 22, 2022 The exponent calculator will calculate the value of any base raised to any power. This page will cover all the related topics, including the negative exponent. Let's start with the basics. What is an exponent?An exponent is a way to represent how many times a number, known as the base, is multiplied by itself. It is represented as a small number in the upper right hand corner of the base. For example: It's easy with small numbers, but for bases that are large numbers, decimals, or when they are raised to a power that's very large or negative, use our tool. If you wish to do exponentiation by hand, do the following:
Negative exponent calculatorThe concept is rather simple when the exponent is positive, but what happens when the exponent is negative? By the definition, if it is -2, we would multiply the base times itself negative two times. In actuality, what is happening here, we take the reciprocal of the base and change the negative exponent to positive and proceed as usual. If you'd like to work it out by hand, do the following:
Here's a quick example: Squaring a base (raising a number to the power of 2) and taking the square root are similar concepts, many people consider one the opposite or the undoing of the other. If you want to
square the number 6, you take Likewise, cubing a base (raising a number to the power of 3) will give us a perfect cube. In case you need to calculate the cube root you can use our cube root calculator which is an excellent tool that will calculate the cube root of any number. In modular arithmetic there are dedicated methods of exponentiation - learn more with the power mod calculator. Besides, you may check our logarithm calculator which is the inverse function of the exponent. Any number raised to the power of 0 equals 1. The negative exponent calculator is useful when dealing with exponential decay, which has a negative exponent in its formula. Mateusz Mucha and Piotr Małek AntilogChange of base formulaCondense logarithms… 11 more How do you solve 1 2 to the 2nd power?1/2 to the power of 2 can be written as (1/2)2, where 1/2 is called the base and 2 is the power of the expression. Therefore, we can rewrite (1/2)2 = 1/2 × 1/2. ⇒ 1/2×1/2 = 1/4 or 0.25.
What does a raise to the power 1/2 mean?Fractional powers
Raising to the power 1/2 means we find the square root, the number which multiplied by itself gives our original number. This another example of mathematicians extending things. We can see why this is if we multiply 3½ by 3½. We get 3½ × 3½ = 3½+½ = 31 = 3. So 3½ must be the square root of 3.
What does 9 to the power of 1/2 mean?Thus, 9 to the power of 1/2 is 3.
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