Question

5) Simplify

a) 25 3/2 x 243 3/5
b) (625) 1/4 - 4 x( 64) 1/3 + 20 x ( 32) 1/5

16 5/4 x 8 4/3

c) 63 1/2 - 5 x (28) 1/2 + 11 x (7) 1/2​

Answer 1

Answer:

a. see the equation in the pic.

b. To simplify:

${ {(625)}^{ \frac{1}{2}) } } ^{ \frac{1}{4} } )^{2}$

powers have to be multiplied

Consider the powers

$( \frac{ - 1}{2} ) \times ( \frac{ - 1}{4} ) ^{2} = ( \frac{ - 1}{2} \times \frac{ - 1}{4} ) \times 2$

$= (\frac{ - 1}{2} ) \times ( \frac{ - 1}{2} ) = \frac{1}{4}$

${(625)}^{ \frac{1}{4} } = (5 \times 5 \times 5 \times 5)^{ \frac{1}{4} }$

$= (5)^{4} \times ( \frac{1}{4} )$

Therefore

${(625)}^{ \frac{ - 1}{2}}^({ \frac{1}{4} } )^{2}$

c.Given :

6 by 3/10 - 2 by 3/4 - 1 by 2/5

This is in mixed fraction, so first of all we have to convert it in improper fraction.

6 by 3/10 = {(10*6) + 3}/10

(60 + 3 )/10

= 63/10

2 by 3/4 = {(4*2) + 3}/4

= (8 + 3)/4

= 11/4

1 by 2/5 = {(5*1) + 2}/5

= (5 + 2)/5

= 7/5

Now, we will take the L. C. M. of 10, 4 and 5, which is 20

63/10

= (20/10)*63

= 2*63

126/20

11/4

= (20/4)*11

= 5*11

= 55/20

7/5

= (20/5)*7

= 4*7

= 28/20

Now,

126/20 - 55/20 - 28/20

= 126/20 - 83/20

= 43/20

= 2 by 3/20

Step-by-step explanation:

hope it helps MRK ME As BRAINLIEST