Expressions involving and powers can seem daunting at first, but with some practice and understanding of the basic rules, they can become much easier to tackle. In this article, we will guide you through the steps to effectively work with that combine fractions and powers.

Let’s start by understanding the different components of such expressions. A fraction is a numerical value that represents a part of a whole, expressed as one number divided by another, for example, 1/2 or 3/4. On the other hand, a power consists of a base raised to an exponent, like 2^3 or 4^2. Expressions combining these elements require careful manipulation to simplify or them.

To simplify expressions with fractions and powers, it is helpful to remember the following rules:

1. Multiplying fractions: When multiplying fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together. For example, (1/2) * (3/4) equals 3/8.

2. Dividing fractions: To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For instance, (2/3) ÷ (4/5) can be simplified as (2/3) * (5/4), resulting in 10/12, which simplifies further to 5/6.

3. Simplifying exponents: When multiplying powers with the same base, add their exponents. For instance, (2^3)*(2^2) equals 2^(3+2) which simplifies to 2^5.

Now that we have a grasp on the basic rules, let’s work through an example:

Consider the expression (3/4)^2 ÷ (2/3)^-1

Step 1: Evaluate the powers individually.
(3/4)^2 simplifies to (3^2)/(4^2), resulting in 9/16.
(2/3)^-1 means taking the reciprocal of the expression, so it becomes 3/2.

Step 2: Divide the two fractions.
To divide fractions, simply multiply the first fraction by the reciprocal of the second fraction. Therefore, (9/16) ÷ (3/2) is equivalent to (9/16) * (2/3). This gives us (18/48).

Step 3: Simplify the fraction.
To simplify (18/48), we divide both the numerator and denominator by their greatest common divisor, which is 6. So, (18/48) simplifies to (3/8).

Hence, the simplified form of the given expression is (3/8).

Once you understand the underlying principles and rules, expressions with fractions and powers become more approachable. Remember to take your time and practice, as that is the key to mastering this subject. With time and effort, you’ll find yourself becoming more proficient in handling such mathematical expressions.

Quest'articolo è stato scritto a titolo esclusivamente informativo e di divulgazione. Per esso non è possibile garantire che sia esente da errori o inesattezze, per cui l’amministratore di questo Sito non assume alcuna responsabilità come indicato nelle note legali pubblicate in Termini e Condizioni
Quanto è stato utile questo articolo?
0Vota per primo questo articolo!