Question

How do you simplify `[\frac { 16\times 45\times 10^ { 3} } { \pi \times 90\times 10^ { 6} } ]`?

Answer 1

The final result is `1/(125pi)`.

Explanation:

`frac { 16\times 45\times 10^ { 3} } { \pi \times 90\times 10^ { 6} }`

Start with the two clearest moves: `45/90` and `10^3/10^6`:

`frac { 16 } { \pi \times 2\times 10^ { 3} }`

Now rewrite `16=2^4`

`frac { 2^4 } { \pi \times 2\times 10^ { 3} }`

We can rewrite `10^3` as `(2*5)^3=2^3*5^3`

`frac { 2^4 } { \pi \times 2\times 2^3 times 5^3 }`

Notice that `2^4` appears in the numerator and denominator since `2 times 2^3 = 2^4` and simplify that:

`frac { 1} { \pi times 5^3 }`

So the final result is `1/(125pi)`