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Introduction and Value of Pi

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Question

$\frac{(8^{3 a} \times 2^{5} \times 2^{2 a})}{(4 \times 2^{11 a} \times 2^{(- 2 a)})}$

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Solution

$\frac{(8^{3 a} \times 2^{5} \times 2^{2 a})}{(4 \times 2^{11 a} \times 2^{(- 2 a)})}$

It can be simplified as:

$\frac{(8^{3 a} \times 2^{5} \times 2^{2 a})}{(4 \times 2^{11 a} \times 2^{(- 2 a)})}$ = $\frac{(2 \times 2 \times 2)^{3 a} \times 2^{5} \times 2^{2 a})}{(2 \times 2) \times 2^{11 a} \times 2^{(- 2 a)})}$
= $\frac{((2^{3})^{3 a} \times 2^{5} \times 2^{2 a})}{(2^{2} \times 2^{11 a} \times 2^{(- 2 a)})}$
= $\frac{(2^{9 a} \times 2^{5} \times 2^{2 a})}{(2^{2} \times 2^{11 a} \times 2^{(- 2 a)})}$
On further calculation, we have
= $\frac{(2^{9 a + 2 a} \times 2^{5})}{(2^{2} \times 2^{11 a - 2 a})}$
= $\frac{(2^{9 a + 2 a + 5})}{(2^{11 a - 2 a + 2})}$
= $\frac{(2^{11 a + 5})}{(2^{9 a + 2})}$
[∵ $\frac{a^{m}}{a^{n}} = a^{(m - n)}$ ]
= $2^{11 a + 5 - 9 a - 2}$
= $2^{2 a + 3}$

Hence, the simplified value is $2^{2 a + 3}$ .

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$6 a^{2} - 13 a + 6 = ? (a) (2 a + 3) (3 a - 2) (b) (2 a - 3) (3 a + 2) (c) (3 a - 2) (2 a - 3) (d) (3 a + 1) (2 a - 3)$

\frac{8^{3 a} \times 2^{5} \times 2^{2 a}}{4 \times 2^{11 a} \times 2^{- 2 a}}

\frac{8^{3 a} \times 2^{5} \times 2^{2 a}}{4 \times 2^{11 a} \times 2^{- 2 a}}

\frac{8^{3 a} \times 2^{5} \times 2^{2 a}}{4 \times 2^{11 a} \times 2^{- 2 a}}

2^{2 a + 3}

State true or false:

Q. Simplified form of

\frac{8^{3 a} \times 2^{5} \times 2^{2 a}}{4 \times 2^{11 a} \times 2^{- 2 a}}

2^{2 a + k}

then the value of

k

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Introduction and Value of Pi

Standard VII Mathematics

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