Question

Which expression has the same value as m-4 + 1/5-4

choices:
a) 1/m* 1/m* 1/m* 1/m + 5*5*5*5
b) m-4 + 1/5-4
c) 1/m* 1/m *1/m *1/m + 4*4*4*4*4
d) 1/m* 1/m *1/m *1/m + 1/5 * 1/5 * 1/5 * 1/5

Answer 1

if its m-4 + 1/5-4, it's b
if you meant m^-4 + (1/5)^-4, it should be a

Answer 2

`(1)/(m)* (1)/(m)* (1)/(m)* (1)/(m)+5* 5* 5* 5`

`m^(-4)+(1)/(5^(-4))`

Explanation:

Given expression,

`m^(-4)+(1)/(5^(-4))`

In option a),

`(1)/(m)* (1)/(m)* (1)/(m)* (1)/(m)+5* 5* 5* 5`

By using product rule of exponent,

`(1)/(m^(1+1+1+1))+5^(1+1+1+1)`

`=(1)/(m^4)+5^4`

By using
`a^m=(1)/(a^(-m))`

`=m^(-4)+(1)/(5^(-4))`

Similarly, in option c),

`(1)/(m)* (1)/(m)* (1)/(m)* (1)/(m)+4* 4* 4* 4`

`(1)/(m^(1+1+1+1))+4^(1+1+1+1)`

`=(1)/(m^4)+4^4`

`=m^(-4)+(1)/(4^(-4))`

In option d)

`(1)/(m)* (1)/(m)* (1)/(m)* (1)/(m)+(1)/(5)* (1)/(5)* (1)/(5)* (1)/(5)`

`(1)/(m^(1+1+1+1))+(1)/(5^(1+1+1+1))`

`=(1)/(m^4)+(1)/(5^4)`

Hence, option a) and b) are correct.