प्लान

घातांक कैलकुलेटर

65 का वर्ग 4,225 है (65 × 65)। यह घात कैलकुलेटर किसी भी संख्या की कोई भी घात निकालता है — पूर्ण, ऋणात्मक या भिन्नात्मक — और हर चरण दिखाता है, 9 की घात 9 से लेकर 8⁻⁴ = 1/4096 तक।

ऋणात्मक या भिन्न हो सकता है, जैसे -3 या 2/3

नतीजा

मान डालें और नतीजा देखने के लिए “गणना करें” दबाएँ।

सूत्र

an=a×a×⋯×aa^n = a \times a \times \cdots \times a

n copies of a multiplied together.

a−n=1ana^{-n} = \frac{1}{a^n}

A negative exponent means one over the power.

ap/q=apqa^{p/q} = \sqrt[q]{a^p}

A fractional exponent is a root of a power.

यह कैलकुलेटर कैसे इस्तेमाल करें

  1. Enter the base and the exponent. The exponent can be a whole number, negative, or a fraction like 2/3.
  2. Press Calculate to see the exact answer and the rule used.

हल किए गए उदाहरण

8 to the power 2/3

8^(2/3) is the cube root of 8².

8² = 64, and the cube root of 64 is 4.

Easy: 65 squared

65² = 65 × 65.

65 × 65 = 65 × 60 + 65 × 5 = 3900 + 325 = 4225.

Medium: a negative exponent, 8⁻⁴

A negative exponent means “one over”: 8⁻⁴ = 1 / 8⁴. This is how to express 8⁻⁴ using a positive exponent.

8⁴ = 8 × 8 × 8 × 8 = 4096, so 8⁻⁴ = 1/4096 ≈ 0.000244.

Hard: 1 doubled 30 times

Doubling 30 times multiplies by 2 thirty times: 1 × 2³⁰.

2¹⁰ = 1024, so 2³⁰ = 1024³ = 1,073,741,824 — over a billion.

आम गलतियाँ

  • Multiplying the base by the exponent: 65² is 65 × 65 = 4225, not 65 × 2 = 130.
  • Thinking a negative exponent makes a negative number: 8⁻⁴ is 1/4096, which is positive.
  • Leaving out brackets with negative bases: (−3)² = 9, but −3² = −9.

अक्सर पूछे जाने वाले सवाल

What is 9 to the power of 9?

9⁹ = 387,420,489. It is also 3¹⁸, because 9 = 3².

How do I expand (x + h) cubed?

(x + h)³ = x³ + 3x²h + 3xh² + h³. Multiply (x + h)(x + h) = x² + 2xh + h² first, then multiply that by (x + h).

What is anything to the power 0?

Any non-zero number to the power 0 is 1. 0⁰ is usually taken as 1 too, but some books leave it undefined.

Why can’t I raise a negative number to the power 1/2?

Power 1/2 means square root, and negative numbers have no real square root.

और जानें