Question

State the first five laws of Exponents. Give examples in which you would use each law.

Short answer

The laws of exponent along with the examples are stated below.

Step-by-step solution

Step 1. State the laws of exponent.

The first law states that to multiply the two powers of same number, powers of the same base is added.

$a^m\times a^n=a^{m+n}$

Example:

$\begin{array}{c}{2}^4\times 2^3=2^{4+3}\\ =2^7\end{array}$

The second law states that to divide two powers of same number, power of the same base is subtract.

$\frac{a^m}{a^n}=a^{m-n}$

Example:

width="85">2423=24−3=21

Step 2. State the laws of exponent.

The third law states that to raise a power to the new power, raise a power to the new power is multiplied with the other.

${\left(a^m\right)}^n=a^{m\times n}$

Example:

$\begin{array}{c}{\left(2^4\right)}^3=2^{4\times 3}\\ =2^{12}\end{array}$

The fourth law state that, to raise product to a power, raise each factor to the power.

${\left(ab\right)}^m=a^m\times b^m$

Example:

${\left(2\times 3\right)}^4=2^4\times 3^4$

Step 3. State the laws of exponent.

The fifth law state that to raise a quotient to a power, raise both the denominator and numerator to the power.

${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

Example:

${\left(\frac{3}{2}\right)}^4=\frac{3^4}{2^4}$

Thus, the laws of exponent along with the examples are stated above.