Question

Which expression is equivalent to (21/2 x 2 3/4)^2

Answer 1

`\left(2(1)/(2)\cdot2(3)/(4)\right)^2=\left((2\cdot2+1)/(2)\cdot(2\cdot4+3)/(4)\right)^2=\left((5)/(2)\cdot(11)/(4)\right)^2=\left((55)/(8)\right)^2\\\\=(55^2)/(8^2)=(3025)/(64)`

Answer 2

ANSWER


`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = 47 (17)/(64)`


Step-by-step explanation

To find the expression that is equivalent to

`(2 (1)/(2) * 2 (3)/(4) ) ^(2)`

we need to simplify it.


We convert the mixed numbers to improper fraction as follows.




`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = ( (2 * 2 + 1)/(2) * (2 * 4 + 3)/(4) ) ^(2)`


This will give us,


`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = ( (4 + 1)/(2) * (8 + 3)/(4) )^(2)`



`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = ( (5)/(2) * (11)/(4) )^(2)`


We multiply the expression in the parenthesis on the right hand side to obtain,


`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = ( (55)/(8) )^(2)`


We share the exponent for the numerator and the denominator separately.



`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = \frac{ {55}^(2) }{ {8}^(2) }`



This simplifies to,



`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = \frac{ {3025} }{ {64}}`


We write the final answer as a mixed number to obtain,


`(2 (1)/(2) * 2 (3)/(4) ) ^(2) = 47 (17)/(64)`