Solution - Adding, subtracting and finding the least common multiple
Step by Step Solution
Step 1 :
1.1 10 = 2•5
(10)3 = (2•5)3 = 23 • 53
Equation at the end of step 1 :
(104)
((2•—————)•(105))-(6•(23•53))
3
Step 2 :
Raising to a Power :
2.1 21 multiplied by 23 = 2(1 + 3) = 24
Equation at the end of step 2 :
(104)
((2•—————)•(105))-(24•3•53)
3
Step 3 :
3.1 10 = 2•5
(10)5 = (2•5)5 = 25 • 55
Equation at the end of step 3 :
(104)
((2 • —————) • (25•55)) - (24•3•53)
3
Step 4 :
4.1 10 = 2•5
(10)4 = (2•5)4 = 24 • 54
Equation at the end of step 4 :
(24•54)
((2 • ———————) • (25•55)) - (24•3•53)
3
Step 5 :
(24•54)
Simplify ———————
3
Equation at the end of step 5 :
(24•54)
((2 • ———————) • (25•55)) - (24•3•53)
3
Step 6 :
Multiplying exponents :
6.1 21 multiplied by 24 = 2(1 + 4) = 25
Equation at the end of step 6 :
(25•54)
(——————— • (25•55)) - (24•3•53)
3
Step 7 :
Multiplying exponents :
7.1 25 multiplied by 25 = 2(5 + 5) = 210
Multiplying exponents :
7.2 54 multiplied by 55 = 5(4 + 5) = 59
Equation at the end of step 7 :
(210•59)
———————— - (24•3•53)
3
Step 8 :
Rewriting the whole as an Equivalent Fraction :
8.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
(24•3•53) (24•3•53) • 3
(24•3•53) = ————————— = —————————————
1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
8.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(210•59) - ((24•3•53) • 3) 210•59 - 18000
—————————————————————————— = ——————————————
3 3
Step 9 :
Pulling out like terms :
9.1 Pull out like factors :
210 • 59 - 18000 = 2 • (1 - 9000)
Final result :
2 • (1 + 9000) —————————————— 3
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