Question

The exponent of 2 in the prime factorization of 288 is

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Answer 1

Answer:

The orange divisor(s) above are the prime factors of the number 288. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288. It can also be written in exponential form as 25 x 32.

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Answer 2

Step-by-step explanation:

Given -

• A number 288

To Find -

• Exponent of 2 in the prime factorisation of 288

Now,

288 = 2×2×2×2×2×3×3

→ 2^5 × 3²

Hence,

The exponent of 2 is 5 and exponent of 3 is 2.

Additional information :-

Laws of exponent of Real numbers :

• a^m × a^n = a^m+n

Examples :-

1) 5² × 5³ = 5²+³

→ 5^5

2) 17² × 17² = 17²+²

→ 17^4

• (a^m)^n = a^mn

Examples :-

1) (5²)³ = 5²×³

→ 5^6

2) (4²)¹ = 4²×¹

→ 4²

• a^m ÷ a^n = a^m-n, m > n

Examples :-

1) 5³ ÷ 5² = 5³-²

→ 5¹

2) 23^10 ÷ 23^7 = 23^10-7

→ 23³

• a^mb^m = (ab)^m

Examples :-

1) 7³ × 9³ = (7×9)³

→ 63³

2) 2^¾ 8^¾ = (2×8)^¾ = (16)^¾

→ 2^4×¾

→ 2³

here, a, n, m are natural numbers.

a is called base and m and n are the exponents.