Question

Simplify the complex fraction.

15t4
16r
(30) 2
Step 1
Simplify the numerator.
15
(3712
PL​

Answer 1

Given:

`$(\left(((4 r)^(3))/(15 t^(4))\right))/(\left((16 r)/((3 t)^(2))\right))`

To find:

The simplified fraction.

Solution:

Step 1: Simplify the numerator

`$((4 r)^(3))/(15 t^(4))=(4^3 r^(3))/(15 t^(4))=(64 r^(3))/(15 t^(4))`

Step 2: Simplify the denominator

`$(16 r)/((3 t)^(2))=(16 r)/(3^2 t^(2))= (16 r)/(9 t^(2))`

Step 3: Using step 1 and step 2

`$(\left(((4 r)^(3))/(15 t^(4))\right))/(\left((16 r)/((3 t)^(2))\right))=(\left((64 r^(3))/(15 t^(4))\right))/(\left((16 r)/(9 t^(2)) \right))`

Step 4: Using fraction rule:

`$((a)/(b))/((c)/(d))=(a \cdot d)/(b \cdot c)`

`$(\left((64 r^(3))/(15 t^(4))\right))/(\left((16 r)/(9 t^(2))\right))=(64r^3 \cdot 9t^2)/(16 r \cdot 15 t^4)`

Cancel the common factor r and t², we get

`$=(64 r^(2) \cdot 9 )/(16 \cdot 15 t^2 )`

Cancel the common factors 16 and 3 on both numerator and denominator.

`$=(4 r^(2) \cdot 3 )/( 5 t^2 )`

`$=(12 r^(2) )/( 5 t^2 )`

`$(\left(((4 r)^(3))/(15 t^(4))\right))/(\left((16 r)/((3 t)^(2))\right))=(12 r^(2) )/( 5 t^2 )`

The simplified fraction is
`(12 r^(2) )/( 5 t^2 )`.