To simplify the expression \( \frac{x^5}{x^{-7}} \), you can use the property of exponents that states:

\[
\frac{a^m}{a^n} = a^{m-n}
\]

Here, \( a = x \), \( m = 5 \), and \( n = -7 \). Applying the property, we get:

\[
\frac{x^5}{x^{-7}} = x^{5 - (-7)}
\]

\[
x^{5 + 7} = x^{12}
\]

Therefore, the simplified form of \( \frac{x^5}{x^{-7}} \) is:

\[
x^{12}
\]

Would you like more details or have any questions? Here are some related questions you might consider:

1. How would you simplify \( \frac{x^8}{x^2} \)?
2. What is the result of \( \frac{y^{-3}}{y^{-5}} \)?
3. How do you simplify \( x^0 \)?
4. If \( \frac{x^a}{x^b} = x^{c} \), what is the relationship between \( a \), \( b \), and

Learn how to simplify the exponential expression x⁵/x⁻⁷ using the laws of exponents. This problem covers key algebraic concepts such as exponentiation and simplification of expressions, making it suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation