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How to Put Powers in Calculator

Reviewed by Calculator Editorial Team

Calculating powers is a fundamental mathematical operation that appears in many fields, from basic arithmetic to advanced scientific calculations. This guide will show you how to properly input and interpret power calculations on your calculator.

Basic Exponents

The most common type of power calculation involves raising a number to a positive integer exponent. This is represented as ab, where a is the base and b is the exponent.

Formula: ab = a × a × ... × a (b times)

For example, 34 means 3 multiplied by itself 4 times: 3 × 3 × 3 × 3 = 81.

How to Calculate on a Calculator

  1. Enter the base number (3 in our example)
  2. Press the exponent button (often marked as "xy" or "^")
  3. Enter the exponent (4 in our example)
  4. Press the equals (=) button to get the result (81)

Most scientific calculators have an exponent function. If yours doesn't, you can multiply the base by itself the number of times indicated by the exponent.

Negative Exponents

Negative exponents represent reciprocals. The calculation a-b is equivalent to 1 divided by ab.

Formula: a-b = 1 / ab

For example, 2-3 equals 1 divided by 23, which is 1/8 or 0.125.

How to Calculate on a Calculator

  1. Enter the base number (2 in our example)
  2. Press the exponent button
  3. Enter the negative exponent (-3 in our example)
  4. Press the equals button to get the result (0.125)

Fractional Exponents

Fractional exponents represent roots. The calculation a1/b is equivalent to the b-th root of a.

Formula: a1/b = √[b]a

For example, 161/2 is the square root of 16, which is 4.

How to Calculate on a Calculator

  1. Enter the base number (16 in our example)
  2. Press the exponent button
  3. Enter the fractional exponent (1/2 in our example)
  4. Press the equals button to get the result (4)

Some calculators have a separate root function. If yours doesn't, use the exponent function with fractional exponents.

Scientific Notation

For very large or very small numbers, scientific notation can be used with exponents. This is often represented as a × 10b.

Formula: a × 10b = a multiplied by 10 raised to the power of b

For example, 3.4 × 105 equals 340,000.

How to Calculate on a Calculator

  1. Enter the coefficient (3.4 in our example)
  2. Press the multiplication button (×)
  3. Enter 10
  4. Press the exponent button
  5. Enter the exponent (5 in our example)
  6. Press the equals button to get the result (340,000)

Common Mistakes

When working with powers, there are several common mistakes to avoid:

  • Confusing multiplication with exponentiation (e.g., thinking 2 × 3 is the same as 23)
  • Forgetting that exponents apply only to the number immediately before them (e.g., 2 × 32 is 2 × 9, not 82)
  • Misplacing the decimal point when using scientific notation
  • Assuming that ab is the same as ba (they are not the same)

Always double-check your calculations, especially when dealing with complex exponent operations.

Frequently Asked Questions

What is the difference between multiplication and exponentiation?

Multiplication combines numbers additively (2 × 3 = 6), while exponentiation means multiplying a number by itself (23 = 8).

How do I calculate a power of a negative number?

For even exponents, the result is positive. For odd exponents, the result is negative. For example, (-3)2 = 9 and (-3)3 = -27.

What is the order of operations when dealing with exponents?

Exponents are calculated before multiplication and addition. For example, 2 + 3 × 42 = 2 + 3 × 16 = 50.

How do I calculate a power of a fraction?

Raise both the numerator and denominator to the power. For example, (2/3)3 = 8/27.