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Exponent Calculator

Compute powers, roots, and exponential expressions

2^10

1,024

Scientific

1.024000e+3

1/x^n

9.7656e-4

2 ^ 10

2^10

1,024

Additional Values

Scientific Notation

1.024000e+3

Reciprocal (1/result)

9.765625e-4

2² (square)

4

2³ (cube)

8

Step-by-Step

1.Step 1: Start with 2
2.Step 2: 2^2 = 4
3.Step 3: 2^3 = 8
4.Step 4: 2^4 = 16
5.Step 5: 2^5 = 32
6.Step 6: 2^6 = 64
7.Step 7: 2^7 = 128
8.Step 8: 2^8 = 256
9.Step 9: 2^9 = 512
10.Step 10: 2^10 = 1024

Exponent Rules

x^a × x^b = x^(a+b)
x^a ÷ x^b = x^(a−b)
(x^a)^b = x^(a×b)
x^(−n) = 1 / x^n
x^(1/n) = ⁿ√x
x^0 = 1

Formulas Used

Power (Exponentiation)

x^n = x × x × ... × x (n times)

Multiply the base x by itself n times. For n=0, the result is always 1 (for x ≠ 0).

Where:

x= The base number
n= The exponent (power)

Nth Root

x^(1/n) = the nth root of x

The nth root of x is the number that, when raised to the nth power, equals x. This is equivalent to x raised to the power 1/n.

Where:

x= The number to find the root of (radicand)
n= The root index (2 for square root, 3 for cube root)

Negative Exponent

x^(-n) = 1 / x^n

A negative exponent produces the reciprocal of the base raised to the corresponding positive exponent.

Where:

x= The base number (x ≠ 0)
n= The positive exponent value

Example Calculations

1Power: 2^10

Inputs

Base2
Exponent10

Result

2^101,024

2^10 = 2×2×2×2×2×2×2×2×2×2 = 1,024. This is 1 kilobyte in computing (1 KB = 2^10 bytes).

2Cube Root: 3rd root of 125

Inputs

Number125
Root Index3

Result

3rd root of 1255

The cube root of 125 is 5 because 5^3 = 5×5×5 = 125. In general, the nth root of x^n = x.

3Negative Exponent: 3^(-4)

Inputs

Base3
Exponent-4

Result

3^(-4)0.012346

3^(-4) = 1/3^4 = 1/81 ≈ 0.012346. The negative exponent creates the reciprocal: instead of 81, you get 1/81.

Frequently Asked Questions

Q

How do you calculate x raised to the power of n?

To calculate x^n, multiply x by itself n times. For example, 2^5 = 2 × 2 × 2 × 2 × 2 = 32. For negative exponents, x^(-n) = 1/x^n. For fractional exponents, x^(1/n) is the nth root of x.

  • 2^10 = 1,024 (multiply 2 by itself 10 times)
  • 3^4 = 81 (3 × 3 × 3 × 3)
  • 5^3 = 125 (5 × 5 × 5)
  • Any number to the 0th power = 1 (except 0^0)
  • 10^6 = 1,000,000 (one million)
BaseExponentResultName
2101,024Two to the tenth
35243Three to the fifth
1031,000Ten cubed
2201,048,576Over one million
Q

What are negative exponents?

A negative exponent means you take the reciprocal of the base raised to the positive exponent. So x^(-n) = 1/x^n. For example, 2^(-3) = 1/2^3 = 1/8 = 0.125. Negative exponents create fractions less than 1.

  • 2^(-1) = 1/2 = 0.5
  • 10^(-2) = 1/100 = 0.01
  • 5^(-3) = 1/125 = 0.008
  • 3^(-4) = 1/81 ≈ 0.0123
ExpressionEqualsDecimal
2^(-1)1/20.5
2^(-3)1/80.125
10^(-3)1/10000.001
5^(-2)1/250.04
Q

How do you calculate nth roots?

The nth root of x is the number that, when raised to the nth power, gives x. It equals x^(1/n). The square root is the 2nd root, cube root is the 3rd root. For example, the 4th root of 16 is 2 because 2^4 = 16.

  • Square root of 144 = 12 (12² = 144)
  • Cube root of 27 = 3 (3³ = 27)
  • 4th root of 256 = 4 (4⁴ = 256)
  • 5th root of 100,000 = 10 (10⁵ = 100,000)
Root TypeOf NumberResult
Square root648
Cube root1255
4th root813
5th root322
Q

What are the key exponent rules?

The fundamental exponent rules are: product rule (x^a × x^b = x^(a+b)), quotient rule (x^a / x^b = x^(a-b)), power rule ((x^a)^b = x^(ab)), and zero rule (x^0 = 1). These rules let you simplify complex expressions.

  • Product: x^a × x^b = x^(a+b)
  • Quotient: x^a ÷ x^b = x^(a−b)
  • Power of a power: (x^a)^b = x^(a×b)
  • Zero exponent: x^0 = 1 for all x ≠ 0
  • Negative: x^(−n) = 1/x^n
RuleFormulaExample
Productx^a × x^b = x^(a+b)2³ × 2⁴ = 2⁷ = 128
Quotientx^a / x^b = x^(a-b)3⁵ / 3² = 3³ = 27
Power(x^a)^b = x^(ab)(2³)² = 2⁶ = 64
Q

What is scientific notation and how does it relate to exponents?

Scientific notation expresses numbers as a coefficient (1-10) times a power of 10. For example, 1,500,000 = 1.5 × 10^6 and 0.0003 = 3 × 10^(-4). It uses exponents to handle very large or very small numbers compactly.

  • 1,000,000 = 1 × 10^6
  • 299,792,458 = 2.998 × 10^8 (speed of light m/s)
  • 0.000001 = 1 × 10^(−6)
  • Positive exponent = large number, negative = small number
NumberScientific NotationPower of 10
1,0001 × 10³3
0.0011 × 10⁻³-3
6,022 × 10²³Avogadro's number23

Understanding Exponents and Powers

Exponents are a fundamental mathematical operation that represents repeated multiplication. When we write x^n (x raised to the power n), we mean multiplying x by itself n times. This compact notation is essential for expressing very large numbers, very small numbers, and complex mathematical relationships.

Beyond simple integer powers, exponents extend to negative values (reciprocals), fractions (roots), and even irrational numbers. The rules of exponents — product rule, quotient rule, and power rule — provide powerful tools for simplifying algebraic expressions and solving equations.

Our exponent calculator handles all cases: positive integer powers with step-by-step multiplication, negative exponents showing reciprocal computation, nth roots, and automatic scientific notation conversion. Whether you are studying algebra or working with scientific data, this tool provides complete results instantly.

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Last Updated: Mar 9, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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