Raise a base number to any power.
Supports whole, negative and fractional exponents — negative gives a reciprocal, fractional gives a root.
Power: base^exponent
An exponent calculator raises a base number to a power. You type the base, such as 1.08, and the exponent, such as 15, and it returns 1.08 multiplied by itself fifteen times. It also accepts negative exponents, which give reciprocals, and fractional exponents, which give roots.
Students meet powers in Class 8 and use the laws of exponents all the way through Class 12, physics and chemistry. Outside school, the same operation drives compound interest, population growth, the decay of medicines and radioactive material, and the powers of 2 behind computer memory. When the exponent is large, repeated multiplication by hand is slow and error-prone, and a single slip in one step ruins the answer. The calculator answers one question quickly: what is the base raised to this power?
1. Write the problem as b^n, where b is the base and n is the exponent.
2. If n is a positive whole number, multiply b by itself n times: b^n = b × b × … × b.
3. For large n, use repeated squaring: b², then (b²)² = b⁴, then b⁸, and combine the pieces you need, for example b¹³ = b⁸ × b⁴ × b.
4. If n is negative, work out b^|n| first and then take its reciprocal: b^(−n) = 1 ÷ b^n.
5. If n is a fraction p/q, take the q-th root of b and raise it to the power p: b^(p/q) = (q-th root of b)^p.
6. Remember the special cases: b^0 = 1 for any non-zero b, and b^1 = b.
b^m means m copies of b multiplied together. If you multiply b^m by b^n you simply have m + n copies, so b^m × b^n = b^(m+n). Dividing cancels n copies, so b^m ÷ b^n = b^(m−n). Raising b^m to the power n gives n groups of m copies, so (b^m)^n = b^(mn). These three laws are not separate rules to memorise; they all follow from counting how many times the base appears as a factor.
Once the division law holds, b^m ÷ b^m = b^0 must equal 1, so b^0 = 1. Then b^0 ÷ b^n = b^(−n) must equal 1 ÷ b^n, which is why a negative exponent is a reciprocal. For fractions, (b^(1/2))² = b^1 = b, so b^(1/2) must be the square root of b. These definitions are chosen so that the same laws keep working, not invented arbitrarily. That consistency is what lets the calculator accept any real exponent.
A negative base with a fractional exponent, such as (−8)^0.5, has no real answer, because no real number squared gives −8. The calculator follows JavaScript's Math.pow, which returns an undefined value there. Similarly 0 raised to a negative power would mean dividing by zero. Growth is also fast: 2^10 is 1,024 but 2^1,024 is beyond the largest number a computer's standard floating-point format can store, so the calculator reports such results as too large to display rather than showing a wrong number.
Meera wants to see how many times her money multiplies if it grows by 8% a year for 15 years, so she raises 1.08 to the power 15.
A fractional exponent is a root and a power together: 1.08^15 = 3.172169114
Answer: Answer 3.1721691142; Reciprocal (1 ÷ answer) 0.315241705
Multiplying the base by the exponent, so that 3^4 becomes 12 instead of 81.
Reading −3^2 as (−3)^2. By convention −3^2 means −(3^2) = −9, while (−3)^2 = 9.
Treating a negative exponent as a negative answer. 2^(−3) is 1/8 = 0.125, not −8.
Adding exponents when the bases differ. 2^3 × 3^2 cannot be combined into a single power.
Entering a percentage growth rate as 8 instead of 1.08 when the base should be the growth factor.
Finding the growth factor for compound interest or inflation over many years.
Working with powers of 10 in scientific notation for physics and chemistry.
Computing powers of 2 for memory sizes, subnet host counts and binary place values.
Estimating population growth or bacterial doubling over a number of generations.
Checking square roots and cube roots by using exponents of 1/2 and 1/3.
What does a fractional exponent mean?
It represents a root — base^(1/2) is the square root, base^(1/3) is the cube root, and so on.