To calculate: The simplification , by multiplication or division , of the expressions given below: a) 15y⋅21y b) 625c2d1035c5d3

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Vasquez · Accepted Answer

Step 1  Consider the expression,  15y×21y  As index in both the radicals is same, use the product property of radicals an×bn=abn , where a,b are any real numbers and n&amp;gt;1 is an integer.  15y×21y=15×21×y×y  =(3×5)×(3×7)×(y×y)  =32×35×y2  =(3×y)2×35  Use the product property of radicals, according to which, ann=a for any real number a and any integer n&amp;gt;1.  (3×y)2×35=(3×y)235  =3y35  Therefore, the multiplication of the given expression is 3y35  b) 6255×c2c5×d10d13=6255×c2−5×d10−13  =125×c−3×d93  =53×c−3×(d3)33  Now, simplify the radicand and use the exponent property b−n=1bn and ambm=(ab)m, where a,b are any real number and m,n are integers.  53×c−3×(d3)33=(5d3)3c33  =(5d3c)33  =5d3c  Therefore, the division of the given expression is 5d3c

To calculate: The simplification , by multiplication or division , of the expressions given below:a)\sqrt{15y} \cdot \sqrt{21y}

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