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

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

1. **Identify the terms with negative exponents**:
   - \(x^{-4}\) has a negative exponent.
   - \(5^{-3}\) has a negative exponent.

2. **Rewrite terms with negative exponents by taking their reciprocal**:
   - \(x^{-4}\) becomes \(\frac{1}{x^4}\).
   - \(5^{-3}\) becomes \(\frac{1}{5^3}\).

3. **Substitute these into the original expression**:
   \[
   \frac{x^{-4}}{2^3 \cdot 5^{-3}} = \frac{\frac{1}{x^4}}{2^3 \cdot \frac{1}{5^3}}
   \]

4. **Simplify the expression**:
   - The expression becomes \(\frac{1}{x^4} \cdot \frac{5^3}{2^3}\).

5. **Multiply the numerators and denominators**:
   - This simplifies to \(\frac{5^3}{x^4 \cdot 2^3}\).

Thus, the expression with only positive exponents is:

\[
\frac{5^3}{x^4 \cdot 2^3}
\]

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you simplify expressions with both positive and negative exponents?
2. What is the value of \(5^3\) and \(2^3\)?
3. How would you simplify the expression if \(x\) had a positive exponent?
4. What is the general rule for handling negative exponents in the denominator?
5. How would this expression change if \(x\) was raised to a different negative power?

**Tip**: Always remember that a negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent.

Learn how to rewrite the expression x^-4 / (2^3 * 5^-3) using only positive exponents with a step-by-step solution. This problem covers key concepts in exponents and fractions, showing how to handle negative exponents by taking reciprocals. Suitable for students in Grades 7-9.

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