What an index does
The index says how many times the base multiplies itself. 2 to the power 10 is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2, which is 1024.
An index of 1 leaves the base unchanged, and an index of 0 gives 1 for any base except zero.
Negative indices
A negative index means one over the positive power. 2 to the power -3 is 1/8, which is 0.125.
That is why the calculator also shows the answer as one over the result.
Worked example
2 to the power 10 is 1024, and its reciprocal is 0.0009765625.
3 to the power 4 is 81. Halving the base and doubling the index does not keep the answer the same, because powers grow much faster than the base.
Inputs for the indices calculator
Base
The number being multiplied by itself. It can be negative.
Index (power)
How many times the base multiplies itself. A negative index gives a fraction.
CALCULATOR QUESTIONS
Indices calculator questions
What is 2 to the power 10?
1024. Ten twos multiplied together give 1024.
What does a negative index mean?
It means one divided by the positive power, so 2 to the power -3 is 1/8.
What is anything to the power 0?
1, except zero to the power zero, which is undefined.
Is index the same as exponent?
Yes. UK schools say index or power, US schools say exponent.