Question
Sower rules with negative exponenis Simp. Write your answer using only positive exponents.
Ask by Norris Harmon. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To simplify an expression with negative exponents, rewrite each term with a negative exponent as the reciprocal of that term with a positive exponent. For example, \( x^{-3} \cdot y^{-2} \) becomes \( \frac{1}{x^3 y^2} \).
Solution
To simplify an expression with negative exponents, we can use the following rule:
\[
a^{-n} = \frac{1}{a^n}
\]
This means that any term with a negative exponent can be rewritten as the reciprocal of that term with a positive exponent.
Let's say we have an expression like \( x^{-3} \cdot y^{-2} \). We can simplify it step by step:
1. Rewrite each term with a negative exponent as a positive exponent:
\[
x^{-3} = \frac{1}{x^3}
\]
\[
y^{-2} = \frac{1}{y^2}
\]
2. Substitute these into the expression:
\[
x^{-3} \cdot y^{-2} = \frac{1}{x^3} \cdot \frac{1}{y^2}
\]
3. Combine the fractions:
\[
= \frac{1}{x^3 y^2}
\]
Thus, the expression \( x^{-3} \cdot y^{-2} \) simplifies to \( \frac{1}{x^3 y^2} \) using only positive exponents.
If you have a specific expression you would like to simplify, please provide it, and I can help you with that!
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Simplify this solution Bonus Knowledge
When you're faced with negative exponents, there's a nifty little trick: to convert a negative exponent into a positive one, simply take the reciprocal of the base. For instance, if you have \(x^{-n}\), you rewrite it as \(\frac{1}{x^{n}}\). It's like flipping the number into its happy side! For example, say you've got \(2^{-3}\). Flip it! It becomes \(\frac{1}{2^{3}} = \frac{1}{8}\). This way, you keep things neat and tidy, making math much more cheerful and manageable!
