지수 계산기
65의 제곱은 4,225입니다 (65 × 65). 이 거듭제곱 계산기는 어떤 수든 정수, 음수, 분수 지수로 거듭제곱하고, 9의 9제곱부터 8⁻⁴ = 1/4096까지 모든 단계를 보여 줍니다.
결과
값을 입력하고 계산을 누르면 결과가 표시됩니다.
공식
n copies of a multiplied together.
A negative exponent means one over the power.
A fractional exponent is a root of a power.
이 계산기 사용법
- Enter the base and the exponent. The exponent can be a whole number, negative, or a fraction like 2/3.
- Press Calculate to see the exact answer and the rule used.
풀이 예제
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.
자주 하는 실수
- 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.
자주 묻는 질문
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.