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Exponent




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An exponent tells you the number of times the base appears as a factor. exponentiation.

For example: The exponent in [math]2\cdot2\cdot2[/math] is 3. This can also be written as [math]2^3[/math]. This also may be known as two cubed. The exponent in [math]4\cdot4\cdot4\cdot4\cdot4[/math] is 5. This can also be written as [math]4^5[/math].

Exponents are used in algebra.

It is a number or symbol, placed above and to the right of the expression to which it applies, that indicates the number of times the expression is used as a factor. For example, the exponent 3 in [math]5^3[/math] indicates [math]5 \cdot 5 \cdot 5[/math]; the exponent x in [math](a + b)^x[/math] indicates [math](a + b)[/math] multiplied by itself x times.

Negative exponents

A negative exponent -1 is a way of saying 'divide 1 by this thing'.
This is also known as a reciprocal, so [math]x^{-1}=\frac{1}{x}.[/math]

Negative exponents can also be different from -1. In this case the negative exponent acts like a normal exponent, so [math]x^{-2}=(x^{-1})^2=\left(\frac{1}{x}\right)^{2}=\frac{1}{x^{2}}.[/math]


The formula for a negative exponent in terms of a normal exponent is [math]x^{-a}=\frac{1}{x^{a}}.[/math]

If we also have a multiplication, like in [math]2x^{-a}[/math], it would be written as [math]\frac{2}{x^{a}}.[/math]