Test Index

Indices

Question : 18 of 86

Marks: +1, -0

\frac{6^{12} \times (35)^{28} \times (15)^{16}}{(14)^{12} \times (21)^{11}}

Solution:

Concept:

Express all numbers as products of primes and simplify exponents.

Explanation:

Step 1: Prime factorise each base:

6 = 2 \times 3

35 = 5 \times 7

15 = 3 \times 5

14 = 2 \times 7

21 = 3 \times 7

Step 2: Write the expression in prime factors:

Numerator:

2^{12} \times 3^{12} \times 5^{28} \times 7^{28} \times 3^{16} \times 5^{16} = 2^{12} \times 3^{28} \times 5^{44} \times 7^{28}

Denominator:

2^{12} \times 7^{12} \times 3^{11} \times 7^{11} = 2^{12} \times 3^{11} \times 7^{23}

Step 3: Cancel common factors:

2^{12}

cancels,

3^{28} / 3^{11} = 3^{17}

7^{28} / 7^{23} = 7^{5}

5^{44}

remains.

Step 4: The simplified expression is

3^{17} \times 5^{44} \times 7^{5}

Step 5: Total prime factors = sum of exponents:

17 + 44 + 5 = 66

Answer:

Go to Question:

Prev Question

Next Question