Explanation

We need to have either a common base or a common exponent to solve this problem. Since we can’t make the base common as each base is a prime number, the only way is to make the exponent common for all the expressions.

The minimum exponent value is 50, so we make the exponents of each base equal to 50. Therefore,

5^{250} = (5^{5})^{50}

7^{200} = (7^{4})^{50}

3^{300} = (3^{6})^{50}

11^{50}

2^{600} = (2^{12})^{50}

With the exponents even, if you’re still not sure which base is the greatest, you can simplify the comparison further. For example, you can rewrite 2^{12} as (2 x 2 x 2 x 2 x 2 x 2) x (2 x 2 x 2 x 2 x 2 x 2), which can also be rewritten as 64 x 64, and you can write 7^{4} as 49 x 49.

You can follow this strategy for the rest of the bases in order to make the comparison simpler.

5^{250} = (5^{5})^{50} = (5 x 25 x 25)^{50} = 3125^{50}

7^{200} = (7^{4})^{50} = (49 x 49)^{50} = 2401^{50}

3^{300} = (3^{6})^{50} = (27 x 27)^{50} = 729^{50}

11^{50}

2^{600} = (2^{12})^{50} = (64 x 64)^{50} = 4096^{50}

Again, it should be clear from the intermediate step which base is the greatest. You don't need to multiply it all out as we did above.

The greatest base among all the option is 2^{12}.

**Correct choice is E.**

The minimum exponent value is 50, so we make the exponents of each base equal to 50. Therefore,

5

7

3

11

2

With the exponents even, if you’re still not sure which base is the greatest, you can simplify the comparison further. For example, you can rewrite 2

You can follow this strategy for the rest of the bases in order to make the comparison simpler.

5

7

3

11

2

Again, it should be clear from the intermediate step which base is the greatest. You don't need to multiply it all out as we did above.

The greatest base among all the option is 2

Exponents and roots are increasingly common in GMAT quant, so we thought we would give all of you some extra practice.