Question

How do you evaluate `2^ { - 2} \cdot ( 12\cdot 3) - 5^ { 3}`?

Answer 1

The answer is -116.

Explanation:

`2^ { - 2} xx( 12xx 3) - 5^ { 3}`

`= 1/2^2 xx 36 - 125`

`= 36/4- 125`

`= 9 - 125`

`= -116`

Answer 2

`-116`

Explanation:

`color(blue)(2^(-2))*color(purple)((12*3))-color(red)(5^3)`

To get rid of the negative exponent, we take it to the denominator to get

`1/(2^2)=color(blue)(1/4)`

`12*3=color(purple)(36)`

`5^3=5*5*5=color(red)(125)`

Putting it all together, we get

`1/4*36-125`

`1/cancel4*9cancel36-125`

`=>9-125=-116`

Hope this helps!

Answer 3

`-122`

Explanation:

`2^-2 xx (12 xx 3) - 5^3`

Apply laws of indices:

`1/cancel(2^2) xx cancel(2^2) xx3 -5^3`

`=3-125`

`=-122`