Application Of Exponent And Radical Rules In Simplifying Algebraic Expressions

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Application of Exponent and Radical Rules in Simplifying Algebraic Expressions I need to do 52 and 102 question numbers. 54 . In this problem we have to use power rule of the exponents: We have, = ( 5 4 3 6 ) 1 2 [Given expression] = ( 5 4 ) 1 2 ( 3 6 ) 1 2 [ Distribution of exponents ] = ( 5 ) 4 ∗ ( 1 2 ) ( 3 ) 6 ∗ ( 1 2 ) [ Power rule of exponents ] = 5 2 3 3 [ Simplification ] = 25 27 [Final answer] So, 25 /27 is the answer of above question. This is in the simplest form. 100 . Here we need to use combination of power rule and reciprocal rules . We have: = ( 5 𝑥 − 1 2 ) − 2 [Given expression] = 1 ( 5 𝑥 − 1 2 ) 2 [ Used reciprocal rule of exponent ] = 1 5 2 ( 𝑥 − 1 2 ∗ 2 ) [Power rule of exponent ] = 1 25 𝑥 − 1 [ Simplification ] = 𝑥 25 [ Used reciprocal rule of exponent ] In none of the questions we had used quotient rule or power rule . Quotient rule: a m = a (m – n) a n Power rule: a m * a n = 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 root of the expression.
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