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Basic Math Examples
e36+14e36+14
Step 1
Rewrite e36e36 as (e12)3(e12)3.
(e12)3+14(e12)3+14
Step 2
Rewrite 11 as 1313.
(e12)3+134(e12)3+134
Step 3
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2)a3+b3=(a+b)(a2−ab+b2) where a=e12a=e12 and b=1b=1.
(e12+1)((e12)2-e12⋅1+12)4(e12+1)((e12)2−e12⋅1+12)4
Step 4
Step 4.1
Rewrite e12e12 as (e4)3(e4)3.
((e4)3+1)((e12)2-e12⋅1+12)4((e4)3+1)((e12)2−e12⋅1+12)4
Step 4.2
Rewrite 11 as 1313.
((e4)3+13)((e12)2-e12⋅1+12)4((e4)3+13)((e12)2−e12⋅1+12)4
Step 4.3
Since both terms are perfect cubes, factor using the sum of cubes formula, a3+b3=(a+b)(a2-ab+b2)a3+b3=(a+b)(a2−ab+b2) where a=e4a=e4 and b=1b=1.
(e4+1)((e4)2-e4⋅1+12)((e12)2-e12⋅1+12)4(e4+1)((e4)2−e4⋅1+12)((e12)2−e12⋅1+12)4
Step 4.4
Simplify.
Step 4.4.1
Multiply the exponents in (e4)2(e4)2.
Step 4.4.1.1
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
(e4+1)(e4⋅2-e4⋅1+12)((e12)2-e12⋅1+12)4(e4+1)(e4⋅2−e4⋅1+12)((e12)2−e12⋅1+12)4
Step 4.4.1.2
Multiply 44 by 22.
(e4+1)(e8-e4⋅1+12)((e12)2-e12⋅1+12)4(e4+1)(e8−e4⋅1+12)((e12)2−e12⋅1+12)4
(e4+1)(e8-e4⋅1+12)((e12)2-e12⋅1+12)4(e4+1)(e8−e4⋅1+12)((e12)2−e12⋅1+12)4
Step 4.4.2
Multiply -1−1 by 11.
(e4+1)(e8-e4+12)((e12)2-e12⋅1+12)4(e4+1)(e8−e4+12)((e12)2−e12⋅1+12)4
Step 4.4.3
One to any power is one.
(e4+1)(e8-e4+1)((e12)2-e12⋅1+12)4(e4+1)(e8−e4+1)((e12)2−e12⋅1+12)4
(e4+1)(e8-e4+1)((e12)2-e12⋅1+12)4(e4+1)(e8−e4+1)((e12)2−e12⋅1+12)4
Step 4.5
Multiply -1−1 by 11.
(e4+1)(e8-e4+1)((e12)2-e12+12)4(e4+1)(e8−e4+1)((e12)2−e12+12)4
(e4+1)(e8-e4+1)((e12)2-e12+12)4(e4+1)(e8−e4+1)((e12)2−e12+12)4
Step 5
Step 5.1
Multiply the exponents in (e12)2(e12)2.
Step 5.1.1
Apply the power rule and multiply exponents, (am)n=amn(am)n=amn.
(e4+1)(e8-e4+1)(e12⋅2-e12+12)4(e4+1)(e8−e4+1)(e12⋅2−e12+12)4
Step 5.1.2
Multiply 1212 by 22.
(e4+1)(e8-e4+1)(e24-e12+12)4(e4+1)(e8−e4+1)(e24−e12+12)4
(e4+1)(e8-e4+1)(e24-e12+12)4(e4+1)(e8−e4+1)(e24−e12+12)4
Step 5.2
One to any power is one.
(e4+1)(e8-e4+1)(e24-e12+1)4(e4+1)(e8−e4+1)(e24−e12+1)4
(e4+1)(e8-e4+1)(e24-e12+1)4(e4+1)(e8−e4+1)(e24−e12+1)4
Step 6
The result can be shown in multiple forms.
Exact Form:
(e4+1)(e8-e4+1)(e24-e12+1)4(e4+1)(e8−e4+1)(e24−e12+1)4
Decimal Form:
1.07780788⋅10151.07780788⋅1015