What is the exponent of the base $7$ after simplifying the following expression?

$(2^{5} \times 7^{3} \times 3^{4}) \times (5^{6} \times 2^{7} \times 7^{11}) \times$ $(7^{4} \times 3^{6})$

10

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20

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19

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18

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Solution

The correct option is D $18$
As we need to find the exponent of the base $7$ , separate all the powers with the base $7$ and compute the value.
We get, $7^{3} \times 7^{11} \times 7^{4} = 7^{3 + 11 + 4}$ [Since $a^{m} \times a^{n} = a^{m + n}$ , for any non-zero integer $a$ ]
$= 7^{18}$
So, the exponent of the base $7$ is $18$ .

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m

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