Simplify \;36 a³ b² x/27 a b³ y.

Correct Answer is : 4a2x3by\;4 a² x/3 b y3by4a2x

Correct Answer is : 4a2x3by\;4 a² x/3 b y3by4a2x

Test Index

BECE Mathematics 2013 Paper

Question : 9

Total: 40

Simplify

\;\frac{36 a^3 b^2 x}{27 a b^3 y}

Solution:

Method I

Using indices and cancellations

\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{36}{27} \times a^{3-1} \times b^{2-3} \times \;\frac{x}{y}

Note: 9 divides 36, 4 times and 27, 3 times.

\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{4}{3} \times a^2 \times b^{-1} \times \;\frac{x}{y}

But

a^{-b} = \;\frac{1}{a^b}

b^{-1} = \;\frac{1}{b^1} = \;\frac{1}{b}

\;\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{4}{3} \times a^2 \times \;\frac{1}{b} \times \;\frac{x}{y}

\;\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{4 \times a^2 \times 1 \times x}{3 \times b \times y}

\;\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{4 a^2 x}{3 b y}

Method II

Change the indices to multiplication, cancel out and simplify

\;a^3 = a \times a \times a

\;b^2 = b \times b

\;b^3 = b \times b \times b

\;\;\frac{36 a^3 b^2 \times}{27 a b^3 y} = \;\frac{36 \times a \times a \times a \times b \times b \times b \times x}{27 \times a \times b \times b \times b \times y}

\;\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{4 \times 1 \times a \times a \times 1 \times 1 \times x}{3 \times 1 \times 1 \times 1 \times b \times y}

\;\;\frac{36 a^3 b^2 x}{27 a b^3 y} = \;\frac{4 a^2 \times}{3 b y}

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