Calculate a Power
Example Data Table
These examples show the sign pattern created by a negative base.
| Expression | Expanded Form | Result |
|---|---|---|
| (-3)0 | 1 | 1 |
| (-3)1 | (-3) | -3 |
| (-3)2 | (-3) × (-3) | 9 |
| (-3)3 | (-3) × (-3) × (-3) | -27 |
| (-3)4 | (-3) × (-3) × (-3) × (-3) | 81 |
| (-3)5 | (-3) × (-3) × (-3) × (-3) × (-3) | -243 |
Formula Used
Positive exponent: an = a × a × a × ... × a, using n factors.
Negative exponent: a-n = 1 ÷ an, where a is not zero.
For the requested expression, (-3)3 = (-3) × (-3) × (-3). The first two factors equal 9. Then 9 × (-3) = -27.
A negative base with an odd exponent produces a negative result. A negative base with an even exponent produces a positive result.
How to Use This Calculator
- Enter the base. Leave -3 for the supplied calculation.
- Enter a whole-number exponent. Leave 3 for this example.
- Select the decimal precision you need.
- Choose Calculate Power.
- Read the result panel above the form.
- Use the expanded form to check repeated multiplication.
- Download a CSV result or save a printable PDF copy when needed.
Understanding (-3) to the Third Power
The expression (-3) to the third power means (-3) × (-3) × (-3). The exponent tells you how many matching factors to multiply. Here, the base is negative three. The exponent is positive three. Parentheses are essential because they keep the negative sign inside the base. Without parentheses, -33 follows a different order of operations. It means -(33), which is also negative twenty-seven in this special case. However, parentheses still show the intended calculation clearly.
Work Through the Sign
Start with the first two factors. Negative three multiplied by negative three equals positive nine. Then multiply positive nine by negative three. The final product is negative twenty-seven. An odd positive exponent leaves a negative result when the base is negative. An even positive exponent gives a positive result. This pattern helps you review answers before trusting a calculator.
Why Powers Matter
Powers are a compact way to write repeated multiplication. They appear in algebra, science, programming, finance, and measurement. A power can grow fast as the exponent rises. Negative bases add a sign pattern that needs attention. Each multiplication by a negative value flips the sign. That is why the number of factors matters. Odd counts finish negative. Even counts finish positive.
Using the Calculator Well
This calculator accepts a numeric base and an integer exponent. It starts with the requested values, negative three and three. You may change the values to compare similar expressions. For example, enter -3 and 2 to get 9. Enter -3 and 4 to get 81. Enter -3 and -2 to get 1/9. A negative exponent moves the power into the denominator. Zero cannot have a negative exponent because division by zero is undefined.
Use the precision control when your answer contains decimals. Whole-number powers usually display without unnecessary trailing zeros. Small or very large values may use scientific notation. This keeps the result readable. The result panel also displays the expression, the expanded form when possible, and the calculation method. Download the result as a CSV file for records. Use the PDF button to save a printable copy from your browser. Each submission keeps the chosen settings visible for comparison. The reset control restores the original example values quickly. This makes repeated practice simple and organized. It supports quick checks.
Avoid Common Notation Errors
Check the sign before calculating. Confirm that the negative base is enclosed in parentheses. Then confirm the exponent. A common error is treating (-3)3 as 33. Another error is overlooking the difference between (-3)2 and -32. The first equals 9. The second equals -9 because the exponent is evaluated first. Clear notation prevents these mistakes.
Practice With Confidence
This page is useful for homework checks and quick practice. It also helps explain exponent rules in a visible way. Try several odd and even exponents. Observe the changing signs. Use the sample table for a quick reference. Enter values carefully, select a suitable precision, and calculate. Practice carefully, then trust the displayed result every time.
Frequently Asked Questions
1. What is (-3) to the third power?
(-3)3 equals -27. Multiply -3 by itself three times. The first multiplication produces 9. Multiplying 9 by -3 produces -27.
2. Why are parentheses important?
They define the full base as -3. Without them, the exponent applies to 3 first, and the leading minus sign is handled afterward. Clear grouping is important, especially with even exponents.
3. Is -33 equal to (-3)3?
-33 is also -27, but its meaning is different: -(33). Parentheses remain important because (-3)2 is 9, while -32 is -9.
4. Why is the result negative?
The base is negative and the exponent is odd. Each multiplication by a negative number changes the sign. After three factors, the product ends negative.
5. What happens with an even exponent?
A negative base raised to an even exponent gives a positive result. For example, (-3)4 equals 81 because there are four negative factors.
6. What does an exponent of zero mean?
Every nonzero base raised to zero equals 1. For example, (-3)0 equals 1. This calculator does not evaluate 00.
7. Can I use a negative exponent?
Yes. A negative exponent creates a reciprocal. For example, (-3)-2 equals 1 ÷ 9, which is approximately 0.111111.
8. Can a negative base use a decimal exponent?
This calculator uses whole-number exponents. Many decimal exponents with negative bases do not produce real-number results. Whole numbers keep the calculation clear and reliable.
9. Why can the result use scientific notation?
Very large or very small powers are easier to read in scientific notation. The calculator switches formats when ordinary decimal notation becomes impractical.
10. What does the CSV download include?
The CSV file includes the expression, result, base, exponent, selected precision, and expanded calculation. It is useful for notes, records, and spreadsheet work.
11. How should I check my work?
Practice carefully, then trust the displayed result every time.