X to the -4th power over 2 to the 3rd power, and 5 to the -3rd power. First rewrite the expression using only positive exponents.

To rewrite the expression \(\frac{x^{-4}}{2^3 \times 5^{-3}}\) using only positive exponents, follow these steps:

1. **Convert \(x^{-4}\) to a positive exponent**:  
   \(x^{-4} = \frac{1}{x^4}\)

2. **Keep \(2^3\) as it is, since it already has a positive exponent**:  
   \(2^3 = 8\)

3. **Convert \(5^{-3}\) to a positive exponent**:  
   \(5^{-3} = \frac{1}{5^3} = \frac{1}{125}\)

So the expression becomes:
\[
\frac{1}{x^4} \times \frac{1}{8} \times \frac{1}{125}
\]

This can be combined into a single fraction:
\[
\frac{1}{x^4 \times 8 \times 125}
\]

Now simplify:
\[
\frac{1}{1000x^4}
\]

This is the expression rewritten with only positive exponents.

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

1. What are the steps to simplify an expression with multiple terms involving negative exponents?
2. How would you simplify an expression with both negative and fractional exponents?
3. How does the rule \(a^{-n} = \frac{1}{a^n}\) apply in different scenarios?
4. What happens if both the numerator and the denominator have negative exponents?
5. How would you

Learn how to rewrite the expression \(\frac{x^{-4}}{2^3 \times 5^{-3}}\) using positive exponents with a step-by-step solution. This problem covers exponents, negative exponents, and simplifying expressions. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation