Question

(27/125)^-2/3+(625/256)^1/4+(5/4)^0

Answer 1

Answer:

The answer is -  

Step-by-step explanation:

= $(27/125)^{-2/3}$ + $(625/256)^{1/4}$ + $(5/4)^{0}$

= $[(27/125)^{1/3}]^{-2}$[Using rule $a^{n/m}$ = $[(a)^{1/m}]^{n}$] + $\sqrt[4]{625}/\sqrt[4]{256}$ + 1 [We know that anything raised to power 0 is always 1]

= $(3/5)^{-2}$ + 5($\sqrt[4]{625}$ = 5 X 5 X 5 X 5 = 5) / 4($\sqrt[4]{256}$ = 4 X 4 X 4 X 4 = 4) + 1

= $(5/3)^{2}$[Reciprocal of 3/5 to make the power positive] + 5/4 + 1

= 25/9 + 5/4 + 1

Now take L.C.M of the denominators 9,4,1

That is 36

25/9 X 4/4 , 5/4 X 9/9 and 1/1 X 36/36[To make the denominators equal]

100/36 , 45/36 and 36/36

CONTINUE

= 25/9 + 5/4 + 1

= 100/36 + 45/36 + 36/36

= 100 + 45 + 36/36

= 145 + 36/36

= 181/36

Answer 2

Please mark me the Brainliest

Answer:

= $[(\frac{3}{5}) ^{3} ]^\frac{-2}{3}$ + $[(\frac{5}{4})^{4}]^{\frac{1}{4}$ + $(\frac{5}{4})^{0}$

= $(\frac{3}{5})^{-2}$ + $(\frac{5}{4})^{1}$ + 1

= $(\frac{5}{3})^{2}$ + $\frac{5}{4}$ + 1

= $\frac{25}{9}$ + $\frac{5}{4}$ + 1

= $\frac{25*4}{9*4}$ + $\frac{5*9}{4*9}$ + $\frac{1*36}{1*36}$

= $\frac{100+45+36}{36}$

= $\frac{181}{36}$