Question

Express each of the following as a product of prime factors in exponential form:

a) 27 x 96
b) 729 x 64
c) 1331
d) 32 x 243
e) 270

Answer 1

To express each given expression as a product of prime factors in exponential form: a) 27 x 96 = 2^5 x 3^4, b) 729 x 64 = 2^6 x 3^6, c) 1331 = 11^3, d) 32 x 243 = 2^5 x 3^5, e) 270 = 2 x 3^3 x 5

Step-by-step explanation:

1. a) 27 can be written as 3^3 and 96 can be written as 2^5 x 3. Therefore, a) 27 x 96 = (3^3) x (2^5 x 3) = 2^5 x 3^4
2. b) 729 can be written as 3^6 and 64 can be written as 2^6. Therefore, b) 729 x 64 = (3^6) x (2^6) = 2^6 x 3^6
3. c) 1331 can be written as 11^3. Therefore, c) 1331 = 11^3
4. d) 32 can be written as 2^5 and 243 can be written as 3^5. Therefore, d) 32 x 243 = (2^5) x (3^5) = 2^5 x 3^5
5. e) 270 can be written as 2 x 3^3 x 5. Therefore, e) 270 = 2 x 3^3 x 5

Learn more about expressing numbers as a product of prime factors