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Question : 62 of 86

Marks: +1, -0

The value of

\;\frac{2^{16} \times 3^{10} \times 5^{4}}{2^{12} \times 3^{6} \times 5^{3}}

is equal to

2160
6480
648
3240

Solution:

Concept:

Simplify the expression using the law of exponents:

\frac{a^m}{a^n} = a^{m-n}

.

Explanation:

The given expression is

\frac{2^{16} \times 3^{10} \times 5^{4}}{2^{12} \times 3^{6} \times 5^{3}}

.

Subtract exponents for each base in the numerator and denominator:

2^{16-12} = 2^4 = 16

,

3^{10-6} = 3^4 = 81

,

5^{4-3} = 5^1 = 5

.

Multiply the results:

16 \times 81 \times 5 = 16 \times 5 \times 81 = 80 \times 81 = 6480

.

Answer:

6480

, which is option B.

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