Question

Which of the following numbers is the largest: 2^36, 3^30, 5^18, 6^12, 7^8, 8^4? (No calculators!)

Answer 1

Answer:

From the given following number $(2)^{36}$ is the largest.

Step-by-step explanation:

Given: The given number is $(2)^{36} ,(3)^{30} ,(5)^{18} , (6)^{12} , (7)^{8} , (8)^{4}$

To find: The largest number among the following

Solution:

The given number is $(2)^{36} ,(3)^{30} ,(5)^{18} , (6)^{12} , (7)^{8} , (8)^{4}$

  First we have to take HCF for the given number

2 is the common factor then we get 18 , 15, 9, 6 , 4 ,2

HCF ( 36 ,30 ,18 ,12, 8 ,4) = 2

As we know that

$(a^{m})^{n} = a^{mn}$

n = 2

$(2)^{36} = (2^{18} )^{2}$

$(3)^{30} = (3 ^{15} )^{2}$

$(5)^{18} = (5^{9}) ^{2}$

$(6)^{12} = (6^{6} )^{2}$

$(7)^{8} = (7^{4} )^{2}$

$(8)^{4} = (8^{2} )^{2}$

Hence powers are same.

Therefore

$(2^{18} ) > (3 ^{15} ) > (5^{9}) > (6^{6} ) > (7^{4} ) > (8^{2} )$

From the given numbers $(2^{18} )$ is the greatest.

Final answer:

As the result from the given following number $(2)^{36}$ is the largest.

#SPJ2

Answer 2

The given question is that we have to find which number is the largest

the given numbers are

2^36, 3^30, 5^18, 6^12, 7^8, 8^4?

Hence, It is found that the largest number is 3 to the power 30.

# spj2

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