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# Exponent

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

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

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 $5^3$ indicates $5 \cdot 5 \cdot 5$; the exponent x in $(a + b)^x$ indicates $(a + b)$ 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 $x^{-1}=\frac{1}{x}.$

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

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

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