Question

find the value of the expression

Answer 1

the answer is option (d) hope it will help you

Answer 2

$\displaystyle \sf{ \frac{ {4}^{n + 1} \times {20}^{m - 1} \times {12}^{m - n} \times {15}^{m + n + 2} }{ {16}^{m} \times {5}^{2m + n} \times {9}^{m + 1} } } = 5$

Given :

The expression

$\displaystyle \sf{ \frac{ {4}^{n + 1} \times {20}^{m - 1} \times {12}^{m - n} \times {15}^{m + n - 2} }{ {16}^{m} \times {5}^{2m + n} \times {9}^{m + 1} } }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{ {4}^{n + 1} \times {20}^{m - 1} \times {12}^{m - n} \times {15}^{m + n + 2} }{ {16}^{m} \times {5}^{2m + n} \times {9}^{m + 1} } }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ \frac{ {4}^{n + 1} \times {20}^{m - 1} \times {12}^{m - n} \times {15}^{m + n + 2} }{ {16}^{m} \times {5}^{2m + n} \times {9}^{m + 1} } }$

$\displaystyle \sf{ = \frac{ {4 }^{n + 1} \times {(4 \times 5)}^{m - 1} \times {(4 \times 3)}^{m - n} \times {(3 \times 5)}^{m + n + 2} }{ {( {4}^{2} )}^{m} \times {5}^{2m + n} \times {( {3}^{2} )}^{m + 1} } }$

$\displaystyle \sf{ = \frac{ {4 }^{n + 1} \times {4 }^{m - 1} \times {5}^{m - 1} \times {4 }^{m - n} \times { 3}^{m - n} \times {3 }^{m + n + 2} \times { 5}^{m + n + 2} }{ {4}^{2m} \times {5}^{2m + n} \times {3}^{2m + 2} } }$

$\displaystyle \sf{ = {3}^{m - n + m + n + 2 - 2m - 2} \times {4}^{n + 1 + m - 1 + m - n - 2m} \times {5}^{m - 1 + m + n + 2 - 2m - n} }$

$\displaystyle \sf{ = {3}^{0} \times {4}^{0} \times {5}^{1} }$

$\displaystyle \sf{ = 1 \times 1 \times 5 }$

$\displaystyle \sf{ = 5 }$

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