Are fraction and power expressions causing you some headaches? Don’t worry, we’ve got you covered! In this step-by-step guide, we’ll take you through the fundamentals of fraction and power expressions, providing you with all the knowledge you need to master these concepts. By the end of this guide, you’ll be solving complex fraction and power expressions like a pro. Let’s get started!

Understanding Fraction Expressions

Fraction expressions involve numbers or variables separated by a fraction bar, also known as a division symbol. To simplify fraction expressions, remember these key steps:

  • Multiply the numerators (the numbers or variables above the fraction bar).
  • Multiply the denominators (the numbers or variables below the fraction bar).
  • Place the resulting product of the numerators over the product of the denominators.

For example, if we have the fraction expression \(\frac{3}{4} \times \frac{2}{5}\), we follow these steps:

  • The product of the numerators is \(3 \times 2 = 6\).
  • The product of the denominators is \(4 \times 5 = 20\).
  • Therefore, the simplified form of the expression is \(\frac{6}{20}\), which can be further simplified to \(\frac{3}{10}\).

Tackling Power Expressions

Power expressions involve a base number raised to an exponent. Here’s how you can simplify power expressions efficiently:

  • When multiplying two powers with the same base, add the exponents. For example, \(a^2 \times a^3 = a^{(2+3)} = a^5\).
  • When dividing two powers with the same base, subtract the exponents. For instance, \(\frac{b^6}{b^4} = b^{(6-4)} = b^2\).
  • To raise a power to another power, multiply the exponents. For instance, \((c^3)^2 = c^{(3\times 2)} = c^6\).

Let’s apply these rules to simplify the power expression \(2^3 \times 2^2\):

  • Adding the exponents, we get \(2^{(3+2)} = 2^5\).
  • Thus, the simplified form of the expression is \(2^5 = 32\).

Putting It All Together

Now that we have covered the basics of fraction and power expressions, it’s time to bring everything together. To solve an expression that involves both fractions and powers, follow these steps:

  1. Simplify the fraction expression.
  2. Simplify the power expression.
  3. Multiply the simplified fraction expression with the simplified power expression.

For example, let’s solve the expression \(\frac{2}{3} \times 4^2\):

  1. Simplifying the fraction, we have \(\frac{2}{3}\).
  2. Using the power rule, we have \(4^2 = 16\).
  3. Multiplying the fraction \(\frac{2}{3}\) with the power \(16\), we get \(\frac{2}{3} \times 16 = \frac{32}{3}\).

Thus, the simplified form of the expression is \(\frac{32}{3}\).

With the knowledge gained from this step-by-step guide, you are now equipped to tackle any fraction and power expression with confidence. Remember to follow the rules and steps explained here, and practice as much as you can to reinforce your understanding. Good luck, and happy solving!

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