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Solution - Power equations
(2^8*3*5^7)
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Step by Step Solution
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(1): "2.4" was replaced by "(24/10)". 2 more similar replacement(s)
Step 1 :
1.1 10 = 2•5
(10)2 = (2•5)2 = 22 • 52
Equation at the end of step 1 :
144 24
(———•(1010))——•(22•52))
100( 10
Step 2 :
12
Simplify ——
5
Equation at the end of step 2 :
144 12
(——— • (1010)) ÷ (—— • (22•52))
100 5
Step 3 :
Multiplying exponents :
3.1 22 multiplied by 22 = 2(2 + 2) = 24
Raising to a Power :
3.2 52 divided by 51 = 5(2 - 1) = 51 = 5
Equation at the end of step 3 :
144
(——— • (1010)) ÷ 240
100
Step 4 :
4.1 10 = 2•5
(10)10 = (2•5)10 = 210 • 510
Equation at the end of step 4 :
144
(——— • (210•510)) ÷ 240
100
Step 5 :
36
Simplify ——
25
Equation at the end of step 5 :
36
—— • (210•510)) ÷ 240
25
Step 6 :
Multiplying exponents :
6.1 22 multiplied by 210 = 2(2 + 10) = 212
Dividing exponents :
6.2 510 divided by 52 = 5(10 - 2) = 58
Equation at the end of step 6 :
Step 7 :
(212•32•58)
Simplify ———————————
240
Dividing exponents :
7.1 212 divided by 24 = 2(12 - 4) = 28
Dividing exponents :
7.2 32 divided by 31 = 3(2 - 1) = 31 = 3
Dividing exponents :
7.3 58 divided by 51 = 5(8 - 1) = 57
Final result :
(28•3•57)
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