(32)^2/5 × (25)^-3/2 / (27)^-4/3 × (125)^1/3 simplify
Answers
Answer:
(29•310)
———————— = 48372.94080
625
Step-by-step explanation:
Step 1 :
1.1 125 = 53
(125)1 = (53)1 = 53
Equation at the end of step 1 :
(322) (25-3) 53
(—————•—————— ÷ (27-4) ÷ 3)•——
5 2 3
Step 2 :
53
Simplify ——
3
Equation at the end of step 2 :
(322) (25-3) 125
(—————•—————— ÷ (27-4) ÷ 3)•———
5 2 3
Step 3 :
3.1 27 = 33
(27)-4 = (33)(-4) = (3)(-12)
Equation at the end of step 3 :
(322) (25-3) 125
(—————•—————— ÷ (3)(-12) ÷ 3)•———
5 2 3
Step 4 :
4.1 25 = 52
(25)-3 = (52)(-3) = (5)(-6)
Equation at the end of step 4 :
(322) (5)(-6) 125
(—————•——————— ÷ (3)(-12) ÷ 3)•———
5 2 3
Step 5 :
1
Divide —— by 2
56
Equation at the end of step 5 :
(322) 1 125
(—————•—————— ÷ (3)(-12) ÷ 3)•———
5 (56•2) 3
Step 6 :
1
Divide —————— by (3)(-12)
(56•2)
6.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
1 1 1 312
—————— ÷ ——— = —————— • ———
(56•2) 312 (56•2) 1
Equation at the end of step 6 :
(322) 312 125
(————— • —————— ÷ 3) • ———
5 (56•2) 3
Step 7 :
312
Divide —————— by 3
(56•2)
Raising to a Power :
7.1 312 divided by 31 = 3(12 - 1) = 311
Equation at the end of step 7 :
(322) 311 125
(————— • ——————) • ———
5 (56•2) 3
Step 8 :
8.1 32 = 25
(32)2 = (25)2 = 210
Equation at the end of step 8 :
210 311 125
(——— • ——————) • ———
5 (56•2) 3
Step 9 :
210
Simplify ———
5
Equation at the end of step 9 :
1024 311 125
(———— • ——————) • ———
5 (56•2) 3
Step 10 :
Multiplying exponents :
10.1 51 multiplied by 56 = 5(1 + 6) = 57
Dividing exponents :
10.2 210 divided by 21 = 2(10 - 1) = 29
Equation at the end of step 10 :
(29•311) 125
———————— • ———
57 3
Step 11 :
Dividing exponents :
11.1 311 divided by 31 = 3(11 - 1) = 310
Dividing exponents :
11.2 53 divided by 57 = 5(3 - 7) = 5(-4) = 1/54
Final result :
(29•310)
———————— = 48372.94080
625
Answer:
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