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Properties Of Exponents | Algebra Math Help

How We Use Properties of Exponents:

Here is a list and examples of some of the properties of exponents:

\begin{array}{l} {\rm Product\ of\ Powers:}\ a^{m} \times \ a^{n} \ =\ a^{m+n}\\ {\rm Example:}\ 2^{3} \ \times \ 2^{5} \ =\ 2^{8}\\ \\ {\rm Quotient\ of\ Powers:}\ \frac{a^{m}}{a^{n}} =a^{m-n}\\ {\rm Example:}\ \frac{3^{9}}{3^{4}} =3^{9-4} =3^{5}\\ \\ {\rm Power\ of\ a\ Power:}\ \left( a^{m}\right)^{n} =a^{m\times n}\\ {\rm Example:}\ \left( 4^{3}\right)^{2} =4^{3\times 2} =4^{6}\\ \\ {\rm Power\ of\ a\ Product:}\ ( ab)^{m} =a^{m} b^{m}\\ {\rm Example}:\ ( 5\times 7)^{3} =5^{7} \times 5^{3}\\ \\ {\rm Power\ of\ a\ Quotient:} \ \left(\frac{a}{b}\right)^{m} =\frac{a^{m}}{b^{m}}\\ {\rm Examples:} \ \left(\frac{3}{2}\right)^{4} =\frac{3^{4}}{2^{3}}\\ \\ {\rm Zero\ Exponent:}\ a^{0} =1\\ {\rm Example:}\ 11^{0} =1\\ \\ {\rm Negative\ Exponent^{*} :}\ a^{-m} -\frac{1}{a^{m}}\\ {\rm Example:}\ 6^{-2} \ =\ \frac{1}{6^{2}}\\ \\ {\rm Rational\ Exponent:} \ a^{\frac{m}{n}} =\sqrt[n]{a^{m}}\\ {\rm Example:}\ 5^{\frac{2}{3}} =\sqrt[3]{5^{2}}\\ \\ {\rm Reciprocal\ of\ a\ fraction:} \ a^{-1} =\frac{1}{a}\\ {\rm Example:}\ 4^{-1} = \frac{1}{4}\\ \\ \end{array}

1. Problem:

Find the value of m in the expression:

11^{17} \div 11^{9} = 11^m

Solution:

This problem uses the quotient of powers property:

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