Explanation

144 = 2 × 2 × 2 × 2 × 3 × 3, which simplifies to 2⁴ × 3².

This is the correct prime factorization, using only prime numbers.

Explanation

Even numbers end in 0, 2, 4, 6, or 8.

4869 ends in 9, so it is not an even number.

Explanation

The given sequence appears to be obtained by dividing the previous term by 3:

2187 ÷ 3 = 729

729 ÷ 3 = 243

243 ÷ 3 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

Explanation

To find the product:

1. Find the greatest prime factor of 88:

Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88

Greatest prime factor: 11

2. Find the smallest prime factor of 117:

Factors of 117: 1, 3, 9, 13, 39, 117

Smallest prime factor: 3

Product:

11 × 3 = 33

Explanation

The student fails by 22 marks, meaning the passing marks are:

178 + 22 = 200

Since 40% marks are required to pass:

40% of Total Marks = 200

Solving for Total Marks:

Total Marks = (200 × 100) ÷ 40 = 500

Explanation

A prime number has exactly two factors: 1 and itself.

The number 1 is not a prime number because it has only one factor (itself).

Explanation

The odd numbers between 10 and 18 are 11, 13, 15, and 17.

These are the elements that satisfy the given set condition.

Explanation

Total production for Jan-March = 1500 tons × 3 months = 4500 tons

Total production for Jan-April = 4500 tons + 1200 tons = 5700 tons

New average = Total production / Number of months = 5700 tons / 4 months = 1425 tons

Explanation

The given ratio is:

5:10 :: 5:x

This is a proportion, so we can set up an equation:

5/10 = 5/x

Cross-multiply:

5x = 5 × 10

5x = 50

Divide by 5:

x = 50/5

x = 10

Explanation

To find the product of x^a and x^b:

x^a × x^b

Using the rule of exponents that states when multiplying two powers with the same base, add the exponents:

x^(a + b)