Computing expressions with fractions and powers can seem daunting at first, but with a clear understanding of the rules and some practice, you’ll be able to breeze through these calculations. In this blog post, we’ll explore the step-by-step process of computing expressions that involve both fractions and powers. Let’s dive in!

Step 1: Simplify any fraction expressions

If your expression contains fractions, start by simplifying them. To simplify a fraction, look for any common factors between the numerator and the denominator, and cancel them out. If possible, further reduce the fraction to its simplest form. Here’s an example:

  • Expression: 2/3 + 4/6
  • Simplifying the fractions: 2/3 + 2/3
  • Adding the fractions: 4/3

Step 2: Apply the power rules

Next, focus on any expressions raised to a power. Use the power rules to simplify them. The power rule states that when you raise an expression to a power, you multiply the exponents. Consider the following example:

  • Expression: (x^2)^3
  • Applying the power rule: x^6

Similarly, when you have multiple expressions raised to the same power, you can apply the power rule to each expression individually. Here’s an example:

  • Expression: (2x^3y^2)^2
  • Applying the power rule: 4x^6y^4

Step 3: Combine like terms

After simplifying fractions and powers, the next step is to combine like terms. If you have multiple terms with the same variables and exponents, you can add or subtract them. Let’s take a look at an example:

  • Expression: 3x^2 + 2x^2
  • Combining like terms: 5x^2

Remember, you can only combine terms that have the same variable(s) and exponent(s).

Step 4: Perform any remaining operations

If your expression still contains any other mathematical operations, such as addition, subtraction, multiplication, or division, perform them following the order of operations (PEMDAS/BODMAS).

Step 5: Check for extraneous solutions

Finally, double-check your solution against any domain or validity restrictions that may be present in the original problem. Sometimes, certain values of variables can result in undefined solutions or create extraneous solutions that do not satisfy the original expression.

By following these steps and practicing regularly, you’ll become more confident in computing expressions with fractions and powers. Remember to take your time, double-check your work, and seek clarity if you encounter any difficulties along the way. Happy computing!

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