Question

find the value of {(81/16)^-3/4 * (25/9)^-3/2 * (2/5)^-3} / (125^2/3 * 8^4/3)

Answer 1

Step by step solution :

Step  1  :

5 Simplify — 2

Equation at the end of step  1  :

81 (25 5 {———•{——— ÷ (—-3) 164 9 2 2

Step  2  :

Equation at the end of step  2  :

81 (25 (5)(-3) {———•{——— ÷ ——————— 164 9 2 (2)(-3)

Step  3  :

25 Simplify —— 9

Equation at the end of step  3  :

81 25 (5)(-3) {———•——— ÷ ——————— 164 9 2 (2)(-3)

Step  4  :

 4.1     25 = 52

(25)-3 = (52)(-3) = (5)(-6)  4.2     9 = 32 (9)-3 = (32)(-3) = (3)(-6)

Equation at the end of step  4  :

81 (5)(-6) (5)(-3) {———•——————— ÷ 2 ÷ ——————— 164 (3)(-6) (2)(-3)

Step  5  :

(5)(-6) Divide ——————— by 2 (3)(-6)

Equation at the end of step  5  :

81 729 (5)(-3) {——}-3 ÷ 4 • —————— ÷ ——————— 16 (2•56) (2)(-3)

Step  6  :

729 (5)(-3) Divide —————— by ——————— (2•56) (2)(-3)


 6.1    Dividing fractions 

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

729 (5)(-3) 729 (2)(-3) —————— ÷ ——————— = —————— • ——————— (2•56) (2)(-3) (2•56) (5)(-3)

Multiplying exponents :

 6.2    21  multiplied by  23   = 2(1 + 3) = 24

Raising to a Power :

 6.3    53   divided by   56   = 5(3 - 6) = 5(-3) = 1/53

Equation at the end of step  6  :

81 729 {——}-3 ÷ 4 • ———— 16 2000

Step  7  :

81 Simplify —— 16

Equation at the end of step  7  :

81 729 (——)-3) ÷ 4 • ———— 16 2000

Step  8  :

 8.1     81 = 34

(81)-3 = (34)(-3) = (3)(-12)  8.2     16 = 24 (16)-3 = (24)(-3) = (2)(-12)

Equation at the end of step  8  :

(3)(-12) 729 ———————— ÷ 4 • ———— (2)(-12) 2000

Step  9  :

(3)(-12) Divide ———————— by 4 (2)(-12)

Dividing exponents :

 9.1    212   divided by   22   = 2(12 - 2) = 210

Equation at the end of step  9  :

1024 729 ———— • ———— 312 2000

Step  10  :

Dividing exponents :

 10.1    210   divided by   24   = 2(10 - 4) = 26

Dividing exponents :

 10.2    36   divided by   312   = 3(6 - 12) = 3(-6) = 1/36

Final result :

64 ——————— = 0.00070 (36•53)