Exponent & Radical Calculator

Calculate powers, roots, simplify radicals, and convert between notations

Exponent Operations

Base (x):

Exponent (n):

Result

16² = 256

Decimal: 256

Step-by-Step Calculation:

16 raised to the power of 2 equals 16 × 16 = 256

Error: Invalid input. Please check your values.

Radical Operations

Radicand:

Index (n for ⁿ√):

Simplified Radical

√50 = 5√2

Decimal: ≈ 7.07107

Step-by-Step Simplification:

√50 = √(25 × 2) = √25 × √2 = 5√2

Error: Invalid input. Please check your values.

Calculation History

16²

Just now

256
√50

Just now

5√2 ≈ 7.071

Frequently Asked Questions (FAQs) - Exponent & Radical Calculator

What is an Exponent & Radical Calculator?

An Exponent & Radical Calculator is a mathematical tool that computes powers, roots, and radical expressions. It helps solve exponential equations, simplify radicals, calculate square roots, cube roots, and other nth roots quickly and accurately.

How do I use the Exponent & Radical Calculator?

Enter your base number and exponent value into the designated fields. The calculator will compute the result using the formula base^exponent. For example, entering 2 as the base and 3 as the exponent calculates 2³ = 8.

What is the difference between exponents and radicals?

Exponents represent repeated multiplication (x^n), while radicals represent roots (ⁿ√x). They are inverse operations – radicals “undo” exponents. For example, √(x²) = x, and (√x)² = x.

How do you calculate negative exponents?

Negative exponents represent reciprocals. The formula is x^(-n) = 1/(x^n). For example, 2^(-3) = 1/(2³) = 1/8 = 0.125.

What does zero exponent mean?

Any non-zero number raised to the power of zero equals 1. This is expressed as x^0 = 1 (where x ≠ 0). For example, 5^0 = 1 and 100^0 = 1.

How do fractional exponents work?

Fractional exponents represent roots. The formula is x^(m/n) = ⁿ√(x^m). For example, 8^(2/3) = ³√(8²) = ³√64 = 4.

Can I calculate exponents with decimal numbers?

Yes, the calculator handles decimal bases and exponents. For example, 2.5² = 6.25 or 10^1.5 ≈ 31.62.

How do you simplify radicals?

To simplify radicals, factor the number under the root into perfect squares (or cubes for cube roots). Extract factors that are perfect powers. For example, √72 = √(36×2) = 6√2.

What is the square root of a negative number?

Square roots of negative numbers involve imaginary numbers. √(-x) = i√x, where i is the imaginary unit. For real number calculations, negative square roots are undefined.

How do you calculate cube roots?

Cube roots (³√x) find the number that when multiplied by itself three times equals x. For example, ³√27 = 3 because 3×3×3 = 27.

What is an nth root?

An nth root (ⁿ√x) is a number that when raised to the nth power equals x. The calculator can compute any nth root, such as fourth roots, fifth roots, and beyond.

How do you multiply exponents with the same base?

When multiplying exponents with the same base, add the exponents: x^a × x^b = x^(a+b). For example, 2³ × 2⁴ = 2^(3+4) = 2⁷ = 128.

How do you divide exponents with the same base?

When dividing exponents with the same base, subtract the exponents: x^a ÷ x^b = x^(a-b). For example, 5⁵ ÷ 5² = 5^(5-2) = 5³ = 125.

What is the power of a power rule?

When raising a power to another power, multiply the exponents: (x^a)^b = x^(a×b). For example, (3²)³ = 3^(2×3) = 3⁶ = 729.

How do you add or subtract radicals?

You can only add or subtract radicals with the same index and radicand (like radicals). For example, 3√2 + 5√2 = 8√2, but √2 + √3 cannot be simplified further.

Where are exponents and radicals used in real life?

Exponents and radicals are used in compound interest calculations, population growth modeling, physics formulas, engineering designs, computer science algorithms, and scientific measurements.

Why is Exponent & Radical Calculator useful for students?

This Exponent & Radical Calculator helps students verify homework answers, understand exponential patterns, check complex calculations, and learn the relationship between exponents and radicals through instant results.

Can Exponent & Radical Calculator help with scientific notation?

Yes, the Exponent & Radical Calculator handles very large and very small numbers using exponential notation, making it useful for scientific and engineering calculations.