How do you calculate 0.009 to the power of -1?

A negative exponent means the reciprocal: 0.009^-1 = 1 / (0.009^1) = 111.111111111111.

0.009 to the power of -1 = 111.111111111111

Q: What is 0.009 to the power of -1?

0.009 to the power of -1 = 111.111111111111.

Q: What does a negative exponent mean?

A negative exponent means the reciprocal of the base raised to the positive exponent: b^-n = 1 / b^n. For example, 2^-3 = 1/2^3 = 1/8 = 0.125.

Quick Answer

0.009 to the power of -1 = 111.111111111111

= 1 / 0.009¹ = 111.111111111111 (negative exponent → reciprocal)

Exponents Calculator

Squared (n²) Cubed (n³) √n ∛n Exponents (bⁿ)

Step-by-Step: 0.009 to the power of -1

A negative exponent means the reciprocal of the base raised to the positive exponent. The general rule is b⁻ⁿ = 1 / bⁿ.

Rewrite with positive exponent: 0.009^-1 = 1 / 0.009¹
Expand the denominator: 1 / 0.009
Compute: 1 / 0.009¹ = 111.111111111111

0.009 to the power of -1 = 111.111111111111

Reciprocal of 0.009

An exponent of -1 means the reciprocal:

0.009^-1 = 1 / 0.009 = 111.111111111111

Table of Powers of 0.009

n	0.009ⁿ
-5	16935087808.43028671103659672475
-4	152415790.27587258039932937
-3	1371742.11248285322359
-2	12345.679012345679
-1	111.111111111111
0	1
1	0.009
2	0.000081
3	0.000000729
4	0.000000006561
5	0.000000000059049
6	0.000000000000531441
7	0.000000000000004782969
8	0.000000000000000043046721
9	0.000000000000000000387420489
10	0.000000000000000000003486784401

Nearby Exponent Examples

Expression	Result
2²	4
2³	8
3²	9
2⁴	16
3³	27
2⁵	32

Notation and Properties of Exponents

The expression bⁿ is read as "b to the power of n", where b is the base and n is the exponent. Several common-language equivalents:

b² = "b squared" (the area of a square with side b)
b³ = "b cubed" (the volume of a cube with edge b)
bⁿ = "b to the nth" (general usage)

Key rules

Zero Rule: b⁰ = 1 for any b ≠ 0
One Rule: 1ⁿ = 1 for any n
Negative exponent: b⁻ⁿ = 1 / bⁿ
Fractional exponent: b^1/n = ⁿ√b (e.g. b^0.5 = √b)
Product rule: b^m × bⁿ = b^m+n
Power rule: (b^m)ⁿ = b^m·n

Constants supported

This calculator accepts the mathematical constants pi (π ≈ 3.14159) and e (Euler's number ≈ 2.71828), with optional leading minus (-pi, -e) for negative variants.

References

Sample Exponent Calculations

Calculate powers of these numbers:

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Squared (n²) — exponent fixed at 2
Cubed (n³) — exponent fixed at 3
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Cube Root (∛n) — exponent fixed at 1/3
Logarithm Calculator — the inverse of exponentiation