Question 25

Fill in the blanks to make the statements true.
${(\frac{11}{15})}^{4} \times__= {(\frac{11}{15})}^{9}$

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Solution

Let ${(\frac{11}{15})}^{4} \times x = {(\frac{11}{15})}^{9}$
${(\frac{11}{15})}^{4} \times x = {(\frac{11}{15})}^{9} \Rightarrow x = \frac{{(\frac{11}{15})}^{9}}{{(\frac{11}{15})}^{4}} \Rightarrow x = {(\frac{11}{15})}^{9} {(\frac{11}{15})}^{- 4} \Rightarrow x = {(\frac{11}{15})}^{9 - 4} \Rightarrow x = {(\frac{11}{15})}^{5}$

Hence, ${(\frac{11}{15})}^{4} \times {(\frac{11}{15})}^{5} = {(\frac{11}{15})}^{9}$

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