Application Of Exponent And Radical Rules In Simplifying Algebraic Expressions

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Application of Exponent and Radical Rules in Simplifying AlgebraicExpressionsI need to do 52 and 102 question numbers.54.In this problem we have to usepower ruleof the exponents:We have,=(5436)12[Given expression]=(54)12(36)12[Distribution of exponents]=(5)4∗(12)(3)6∗(12)[Power rule of exponents]=5233[Simplification]=2527[Final answer]So, 25/27is the answer of above question. This is in the simplest form.100.Here we need to use combination ofpowerruleand reciprocal rules.We have:=(5𝑥−12)−2[Given expression]=1(5𝑥−12)2[Used reciprocal rule of exponent]=152(𝑥−12∗2)[Power rule of exponent]=125𝑥−1[Simplification]=𝑥25[Usedreciprocal rule of exponent]In none of the questions we had usedquotient ruleorpowerrule.Quotient rule:am= a(m–n)anPowerrule:am* an= a(m + n).Principal root:Sometimes in case of index of radical is even we get two solutions, in that case positive answer is the principal rootof the expression.

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