Question

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

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

Answer:

$\frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}+5\times 5\times 5\times 5$

$m^{-4}+\frac{1}{5^{-4}}$

Step-by-step explanation:

Given expression,

$m^{-4}+\frac{1}{5^{-4}}$

In option a),

$\frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}+5\times 5\times 5\times 5$

By using product rule of exponent,

$\frac{1}{m^{1+1+1+1}}+5^{1+1+1+1}$

$=\frac{1}{m^4}+5^4$

By using $a^m=\frac{1}{a^{-m}}$

$=m^{-4}+\frac{1}{5^{-4}}$

Similarly, in option c),

$\frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}+4\times 4\times 4\times 4$

$\frac{1}{m^{1+1+1+1}}+4^{1+1+1+1}$

$=\frac{1}{m^4}+4^4$

$=m^{-4}+\frac{1}{4^{-4}}$

In option d)

$\frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}\times \frac{1}{m}+\frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}\times \frac{1}{5}$

$\frac{1}{m^{1+1+1+1}}+\frac{1}{5^{1+1+1+1}}$

$=\frac{1}{m^4}+\frac{1}{5^4}$

Hence, option a) and b) are correct.