exponent, in mathematics, a number, letter, or algebraic expression written above and to the right of another number, letter, or expression called the base. In the expressions x² and xⁿ, the number 2 and the letter n are the exponents respectively of the base x. The exponent indicates the power to which the base is to be raised. When exponents were first introduced, only positive whole numbers were used, and the exponent indicated how many times the base was to be taken as a factor; e.g., 2⁵=32, or 2·2·2·2·2=32. In advanced algebra, fractions, zero, and negative numbers are also used as exponents. Particular meanings have been assigned to these types of exponents so that they obey the same algebraic rules as does the simpler type of exponent. A fractional exponent such as 1/4 or 1/n indicates the fourth or nth root, respectively, of the base. Any nonzero quantity raised to the zero power equals one; e.g., x⁰=5⁰=(a²+b²)⁰=1. A negative exponent indicates the reciprocal of the quantity; e.g., x^-2 means 1/x². When quantities of the same base are multiplied together, their exponents are added; e.g., x²·x³=x⁵. Note that the base must be the same. When a quantity already containing an exponent is raised to a power, the exponents are multiplied; e.g., (x²)³=x⁶.

The Corrected d-exponent, also known as cd-exponent or more correctly dc-exponent (d_c-exponent) as used in mud logging in the oil industry, is an extrapolation of certain drilling parameters to get a pressure gradient for pore pressure evaluation while drilling into over-pressured zones. It is regarded as one of the best tools for pore pressure evaluation. See mud log for an example of the corrected d-exponent plotted on a mud log.

The parameters used to get dc-exponent values are: drilling rate, rotary speed, bit weight, bit diameter and mud weight; versus well depth.

As a drill bit bores a hole into the earth, it will gradually experience denser formations and therefore slower rates of penetration. (Though there are exceptions such as sands that normally drill faster, or faulted and uplifted formations). The general trend is normally a gradually slowing rate of penetration.

Sands often have above them, an impermeable layer of formation, normally shale, that may be hundreds of feet deep. When gas or fluids migrate up through the sand and reach this impermeable layer and has nowhere else to go, pressure begins to build up in the sand and pushes up against the impermeable layer of shale. Over time the pressure can becomes so great that it begins to fracture the shale, making it weaker and easier to penetrate by a drill bit. When a hole is drilled down towards this sand, it will gradually begin to experience faster rates of penetration as it drills through this shale gets closer to the high-pressure sand. It is this trend that the dc-exponent exposes. An examination of this fractured shale that is being drilled will reveal increasingly larger concave pieces and is where the term pressure shale comes from.