Question

What are the first three laws of exponents?

Answer 1

Laws of Exponents

* Product. When multiplying like bases, keep the base the same and add the exponents. Example:

$x^3\cdot x^5=x^{3+5}=x^8$

* Power to another power: When raising a base with a power to another power, keep the base the same and multiply the exponents. Example:

$(x^3)^5=x^{3\cdot5}=x^{15}$

* Division: When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent. Example:

$\frac{x^{14}}{x^4}=x^{14-4}=x^{10}$

* Zero exponents: A real base raised to the exponent 0 is equal to 1. Examples:

$\begin{gathered} x^0=1 \\ 2^0=1 \end{gathered}$

* Negative Power: When a negative exponent is used to raise a number, convert it to a reciprocal to make the exponent positive. Examples:

$\begin{gathered} x^{-2}=\frac{1}{x^2} \\ \frac{3}{x^{-5}}=3x^5 \end{gathered}$