Rewrite Expression with Positive Exponents Calculator

This calculator helps you rewrite mathematical expressions with negative exponents to equivalent expressions with positive exponents. It follows the fundamental exponent rules to simplify expressions for easier calculation and understanding.

How to Use This Calculator

To use the rewrite expression calculator:

Enter the base number in the first field
Enter the negative exponent in the second field
Click the "Calculate" button
View the rewritten expression with positive exponents

The calculator will display the original expression, the rewritten expression, and a step-by-step explanation of how the conversion was made.

Rules for Rewriting Expressions

When converting expressions with negative exponents to positive exponents, follow these fundamental rules:

Exponent Rule

a⁻ⁿ = 1/aⁿ

This is the primary rule for converting negative exponents to positive exponents.

Combined Exponents

(a·b)⁻ⁿ = a⁻ⁿ·b⁻ⁿ = 1/(aⁿ·bⁿ)

For expressions with multiple bases, apply the exponent to each base individually.

Power of a Power

(aⁿ)⁻ᵐ = a⁻ⁿᵐ = 1/aⁿᵐ

When you have an exponent raised to another exponent, multiply the exponents.

Remember that the base remains the same when converting exponents. Only the exponent sign changes from negative to positive, and the expression is placed in the denominator.

Worked Examples

Example 1: Simple Negative Exponent

Original expression: 5⁻³

Rewritten expression: 1/5³ = 1/125

Explanation: Apply the exponent rule directly. The negative exponent indicates the reciprocal of the base raised to the positive exponent.

Example 2: Combined Bases

Original expression: (2·3)⁻²

Rewritten expression: 1/(2²·3²) = 1/(4·9) = 1/36

Explanation: Apply the exponent to each base individually, then combine them in the denominator.

Example 3: Power of a Power

Original expression: (x²)⁻⁵

Rewritten expression: 1/x¹⁰

Explanation: Multiply the exponents when you have an exponent raised to another exponent.

Frequently Asked Questions

Why do we rewrite expressions with positive exponents?

Rewriting expressions with positive exponents makes them easier to understand and work with. It follows mathematical conventions and simplifies calculations, especially when dealing with complex expressions.

Can I use this calculator for any type of expression?

This calculator is designed for basic expressions with negative exponents. For more complex expressions involving variables or multiple operations, you may need to apply the rules manually.

What if I have a fraction with negative exponents?

For fractions with negative exponents, apply the exponent rule to each part of the fraction separately. For example, (a/b)⁻ⁿ = bⁿ/aⁿ.