Express each of the following as a product of prime factors only in exponential form.
$270$
Last updated date: 27th Mar 2023
•
Total views: 310.8k
•
Views today: 2.88k
Answer
310.8k+ views
Hint: First solve this in prime factorization method and then convert into prime factors of exponential form.
Starting with the first prime number we can write $270$as
$270 = 2 \times 135$
Then converting $135$ into the factors of next prime number $3$we have
$270 = 2 \times 3 \times 45$
Again converting $45$into the prime factors of $3$ we have
$270 = 2 \times 3 \times 3 \times 15$
Now at last converting $15$into the prime factors of $3$and $5$ we have
$270 = 2 \times 3 \times 3 \times 3 \times 5$
Finally, converting them into exponential form we have
\[270 = {2^1} \times {3^3} \times {5^1}\]
Thus, the product of prime factors in the exponential form of \[270\]is \[{2^1} \times {3^3} \times{5^1}\]
Note: In this type of problems first write prime factors of lower prime numbers and then to higher
prime numbers.
Starting with the first prime number we can write $270$as
$270 = 2 \times 135$
Then converting $135$ into the factors of next prime number $3$we have
$270 = 2 \times 3 \times 45$
Again converting $45$into the prime factors of $3$ we have
$270 = 2 \times 3 \times 3 \times 15$
Now at last converting $15$into the prime factors of $3$and $5$ we have
$270 = 2 \times 3 \times 3 \times 3 \times 5$
Finally, converting them into exponential form we have
\[270 = {2^1} \times {3^3} \times {5^1}\]
Thus, the product of prime factors in the exponential form of \[270\]is \[{2^1} \times {3^3} \times{5^1}\]
Note: In this type of problems first write prime factors of lower prime numbers and then to higher
prime numbers.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India
