(2 3/4) to the second power

Question

Please help me with this I’m studying for school

Answer 1

There are two ways of doing this:

First way:

(2 3/4)² = (2 3/4)*(2 3/4)

Change these into improper fractions: (multiply the whole number, 2, by the denominator, 4 and then add the numerator, 3 to get (2*4) + 3 = 11 as the numerator of the improper fraction. The denominator of 4 will still be the same as the denominator of the original function, 4. So, the improper fraction will be 11/4.)

Therefore we have:

(2 3/4)² = (2 3/4)*(2 3/4) = (11/4)(11/4)

(When we multiply fractions we multiply the numerators together to get the numerator and the denominators together to get the denominator.)

So,

(11/4)(11/4) = (11*11)/(4*4) = 121 / 16

We can then turn this back into a mixed number.

16 goes into 121 seven times, and there is a remainder of 9 so our mixed number is 7 9/16.

Or we can use exponential rules:

We convert to an improper fraction:

(2 3/4)² = (11/4)²

By our exponential rules we get:

(11/4)² = 11²/ 4²

= 121 / 16

Then we turn it back into a mixed number: (Again, 16 goes into 121 seven times, and there is a remainder of 9 )

So, our mixed number is 7 9/16.