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:

Concepts

a^{x} x a^{y} = a^{x+y}

, thus if the bases are the same and multiplying, add the powers

(a^x \times b^y)^n = a^{x \times n} \times b^{y \times n}

, thus the outside power multiplies all the powers inside

Applying these two concepts,

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

NOTE: Every number or letter is raised to the power 1 , which has no effect, hence

2 = 2^1

and

a = a^1

\Rightarrow (2 a b^2)^2 \times 3 a^3 b = 4 a^2 b^4 \times 3 a^3 b

Simplifying the numbers and the ones with the same bases

\Rightarrow 4 a^2 b^4 \times 3 a^3 b = 4 \times 3 \times a^2 \times a^3 b^4 x b

Applying concept

1, a^{x} x a^{y} = a^{x+y}

\Rightarrow 4 \times 3 \times a^2 \times a^3 b^4 x b = 12 a^{2+3} b^{4+1} = 12 a^5 b^5

NOTE:

b = b^1 \Rightarrow b^4 x b = b^4 x b^1 = b^{4+1} = b^5

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