Question

simplify 12⁴×9³×4/6³×8²×27

Answer 1

By applying easy method,

12⁴ × 9³ × 4 12*12*12*12*9*9*9*4
_________ = __________________
6³ × 8² × 27 6*6*6*8*8*9*3

By cancelling out some numbers


= 12*9*9*4
________
8*3

= 18*9
= 162

Hope it will help you

Answer 2

The value of expression is 162.

Given:

• $\frac{ {(12)}^{4} \times {9}^{3} \times 4 }{ {6}^{3} \times {8}^{2} \times 27 }$

To find:

• Simplify the expression.

Solution:

Concept/Formula to be used:

1. ${(ab)}^{m} = {a}^{m} \times {b}^{m}$
2. ${a}^{m} \times {a}^{n} = {a}^{(m+n)}$
3. $\frac{ {a}^{m} }{ {a}^{n} } = {a}^{(m-n)}$

Step 1:

Write expression in simple form.

$= \frac{ {(3 \times 4)}^{4} \times {(3 \times 3)}^{3} \times 4 }{ {(2 \times 3)}^{3} \times {(4 \times 2)}^{2} \times {3}^{3} }$

or

Apply rule 1

$= \frac{ {(3) ^{4}\times (4)}^{4} \times {(3)^{3}\times (3)}^{3} \times 4 }{ {(2)^{3}\times (3)}^{3} \times {(4)^{2} \times( 2)}^{2} \times {3}^{3} }$

Step 2:

Apply rule 2

$= \frac{ {(3) ^{10}\times (4)}^{5} }{ {(2)^{5}\times (3)}^{6} \times {(4)^{2} }}$

Step 3:

Apply rule 3

$= \frac{ {(3) ^{10 - 6}\times (4)}^{5 - 2} }{ {(2)^{5} }}$

or

Apply rule 1

$= \frac{ {(3) ^{4}\times (2)}^{6} }{ {(2)^{5} }}$

or

Apply rule 3

$= (3) ^{4}\times {(2)}^{6 - 5}$

or

$= {3}^{4} \times 2$

or

$= 81 \times 2$

or

$= 162$

Thus,

$\bf \red{\frac{ {(12)}^{4} \times {9}^{3} \times 4 }{ {6}^{3} \times {8}^{2} \times 27 } = 162 }$

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