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.Application Of Exponent And Radical Rules In Simplifying Algebraic Expressions
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Mathematics