Simplify: (2 a b²)² × 3 a³ b.

Correct Answer is : 12a5b5\;\; 12 a^5 b^512a5b5

Correct Answer is : 12a5b5\;\; 12 a^5 b^512a5b5

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BECE Mathematics 2020 Paper

Question : 8

Total: 40

Simplify:

(2 a b^2)^2 \times 3 a^3 b

Solution:

Concept:

Use the laws of exponents:

(x^m)^n = x^{m \times n}

and

x^m \times x^n = x^{m+n}

Explanation:

First, expand the bracket using the power of a product rule:

(2ab^2)^2 = 2^2 \times a^2 \times b^{2 \times 2} = 4a^2b^4

Now multiply this result by

3a^3b

4a^2b^4 \times 3a^3b = (4 \times 3) \times a^{2+3} \times b^{4+1}

Since

b = b^1

, the exponent of

b

becomes

4 + 1 = 5

Therefore, the simplified expression is:

12a^5b^5

Answer:

12 a^{5} b^{5}

Option D.

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