Simplify
3^20+3^19 / 3^21-3^20 =2/3
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Answers
Answer:
No
Step-by-step explanation:
Exponentiation: 3 ^ 20 = 3486784401
Exponentiation: 3 ^ 19 = 1162261467
Exponentiation: 3 ^ 21 = 10460353203
Divide: the result of step No. 2 / the result of step No. 3 = 1162261467 / 10460353203 = 0.11111111111111 = 1/
9
Add: the result of step No. 1 + the result of step No. 4 = 3486784401 + 1/
9
= 3486784401/
1
+ 1/
9
= 3486784401 · 9/
1 · 9
+ 1/
9
= 31381059609/
9
+ 1/
9
= 31381059609 + 1/
9
= 31381059610/
9
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(1, 9) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 9 = 9. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - three billion four hundred eighty-six million seven hundred eighty-four thousand four hundred one plus one ninth = thirty-one billion three hundred eighty-one million fifty-nine thousand six hundred ten ninths.
Exponentiation: 3 ^ 20 = 3486784401
Subtract: the result of step No. 5 - the result of step No. 6 = 31381059610/
9
- 3486784401 = 31381059610/
9
- 3486784401/
1
= 31381059610/
9
- 3486784401 · 9/
1 · 9
= 31381059610/
9
- 31381059609/
9
= 31381059610 - 31381059609/
9
= 1/
9
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(9, 1) = 9. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 1 = 9. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - thirty-one billion three hundred eighty-one million fifty-nine thousand six hundred ten ninths minus three billion four hundred eighty-six million seven hundred eighty-four thousand four hundred one = one ninth.
Compare: the result of step No. 7 vs 2/
3
= 1/
9
vs 2/
3
= 1/
9
vs 2 · 3/
3 · 3
= 1/
9
vs 6/
9
= 1 vs 6 = No