Rewrite The Expression with Positive Exponents Calculator

This calculator helps you rewrite mathematical expressions with negative exponents to equivalent expressions with positive exponents. Learn the rules, see examples, and understand how to apply this in algebra and calculus.

How to Use This Calculator

Enter your expression with negative exponents in the input field. The calculator will automatically convert it to an equivalent expression with positive exponents. You can also see the step-by-step process and verify the result.

Tip: For complex expressions, break them down into parts before entering them into the calculator.

Rules for Rewriting Exponents

When rewriting expressions with negative exponents, follow these key rules:

Negative exponent rule: For any non-zero number \( a \) and integer \( n \), \( a^{-n} = \frac{1}{a^n} \).
Combining exponents: When you have multiple negative exponents, combine them using the product of powers rule: \( a^{-m} \times a^{-n} = a^{-(m+n)} \).
Variables in denominators: If a variable is in the denominator, move it to the numerator with a positive exponent: \( \frac{1}{x^{-n}} = x^n \).

Formula: \( a^{-n} = \frac{1}{a^n} \)

Worked Examples

Here are some examples of how to rewrite expressions with negative exponents:

Original Expression	Rewritten Expression
\( 5^{-3} \)	\( \frac{1}{5^3} \) or \( \frac{1}{125} \)
\( x^{-2} \)	\( \frac{1}{x^2} \)
\( \frac{1}{y^{-4}} \)	\( y^4 \)

For more complex expressions, apply the rules step by step. For example, \( \frac{a^{-2}b^3}{c^{-4}} \) becomes \( \frac{c^4b^3}{a^2} \).

Frequently Asked Questions

Why do we need to rewrite expressions with positive exponents?: Rewriting expressions with positive exponents makes them easier to understand and work with, especially when dealing with fractions and variables.
Can I use this calculator for variables with negative exponents?: Yes, the calculator works with both numerical and variable expressions with negative exponents.
What if my expression has multiple negative exponents?: Use the product of powers rule to combine the exponents before applying the negative exponent rule.