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When dealing with exponents, seeing a negative sign can be confusing. But don't worry. You can easily change negative exponents into positive ones. Let's break it down. A negative exponent means you need to "flip" the base. For example, an expression like \( y^{-5/7} \) becomes \( \frac{1}{y^{5/7}} \). This shows that the base, \( y \), is now in the denominator of a fraction. Which is a handy trick to remember: - Convert negative exponents into fractions by flipping the base.- Always rewrite the expression with positive exponents to make it easier to read and solve. With positive exponents, you're working on simplifying the situation from a fraction with a negative exponent to a more manageable form.

Understanding exponent rules makes working with expressions less daunting. There are basic rules you will use frequently: - **Product of Powers Rule**: When you multiply two powers with the same base, you add the exponents. For example, \( a^m \times a^n = a^{m+n} \). - **Quotient of Powers Rule**: When you divide two powers with the same base, you subtract the exponents, like \( \frac{a^m}{a^n} = a^{m-n} \). - **Power of a Power Rule**: When you have an exponent raised to another power, multiply the exponents, as in \((a^m)^n = a^{m \times n} \). In our exercise, we used the rule \( a^{-n} = \frac{1}{a^n} \). This transforms negative exponents into positive ones simplifying the expression. Knowing these rules helps in both simplifying expressions and understanding the steps taken to solve exponent problems.

The art of simplifying expressions lies in making them cleaner and more straightforward. Once you've rewritten negative exponents as positive ones, you're halfway there. Simplification involves: - **Rewriting the Expression**: After converting the negative exponents, adjust the format to be more readable. Like in this exercise, the expression \( \frac{2}{3} \times y^{5/7} \) is now much simpler. - **Combine Like Terms If Possible**: If the expression has like terms, combine them to further simplify. Since there are no like terms in \( \frac{2 \times y^{5/7}}{3} \), it is already in its simplest form.- **Check Your Work**: Ensure that all components of the expression are as simplified as possible. Double-checking helps avoid mistakes.By understanding and following these steps, you can tackle expressions with ease, ensuring they are as reduced and digestible as possible.