Question

Explain some examples of the laws of exponents ?

Answer 1

$\begin{array}{cc}Law& Example\\ x^1=x& 6^1=6\\ x^0=1& 7^0=1\\ x^{-1}=\frac{1}{x}& 4^{-1}=\frac{1}{4}\\ x^m{x}^n=x^{m+n}& x^2{x}^3=x^{2+3}=x^5\\ \frac{x^m}{x^n}=x^{m-n}& \frac{x^6}{x^2}=x^{6-2}=x^4\\ (x^m{)}^n=x^{mn}& (x^2{)}^3=x^{2\times 3}=x^6\\ (xy{)}^n=x^n{y}^n& (xy{)}^3=x^3{y}^3\\ (\frac{x}{y}{)}^n=\frac{x^n}{y^n}& (\frac{x}{y}{)}^2=\frac{x^2}{y^2}\\ x^{-n}=\frac{1}{x^n}& x^{-3}=\frac{1}{x^3}\\ AndthelawaboutFractionalExponents:& \\ x^{\frac{m}{n}}=\sqrt[n]{n{x}^m}& x^{\frac{2}{3}}=\sqrt[3]{3x^2}\\ =(\sqrt[n]{nx}{)}^m& =\left(\sqrt[3]{3x}\right)\end{array}$
For Example :
$2^{3{}^2}=2^{\left(3^2\right)}=5125^6÷5^2=\frac{5^6}{5^2}=\frac{5\times 5\times 5\times 5\times 5\times 5}{5\times 5}5\times 5\times 5\times 5\times 5\times 5^4=5^{6-2}{5}^6÷5^2=5^{6-2}(2\times 3{)}^5=(2\times 3)\times (2\times 3)\times (2\times 3)\times (2\times 3)\times (2\times 3)=(2\times 2\times 2\times 2\times 2)\times (3\times 3\times 3\times 3\times 3)=2^5\times 3^5[(2^2{)}^3\times 3^6]\times 5^6=[2^6\times 3^6]\times 5^6=(2\times 3{)}^6\times 5^6=(2\times 3\times 5{)}^6={30}^6$