Question

12^4*9^3*4/6^3*8^2*27 simplify and write exponential form

Answer 1

Hey friend,
Here is the answer you were looking for:

$\frac{ {12}^{4} \times {9}^{3} \times 4 }{ {6}^{3} \times {8}^{2} \times 27} \\ \\ = \frac{ {3}^{4} \times {2}^{4} \times {2}^{4} \times {3}^{3} \times {3}^{3} \times {2}^{2} }{ {2}^{3} \times {3}^{3} \times {2}^{2} \times {2}^{2} \times {2}^{2} \times {3}^{3} } \\ \\ using \: the \: identity \\ {a}^{m} \times {a}^{n} = {a}^{m + n} \\ = \frac{ {2}^{4 + 4 + 2} \times {3}^{4 + 3 + 3} }{ {2}^{3 + 2 + 2 + 2} \times {3}^{3 + 3} } \\ \\ = \frac{ {2}^{10} \times {3}^{10} }{ {2}^{9} \times {3}^{6} } \\ \\ using \: the \: identity \\ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ = {2}^{10 - 9} \times {3}^{10 - 6} \\ \\ = {2}^{1} \times {3}^{4} \\ \\ = 2 \times {3}^{4}$

Hope this helps!!!

@Mahak24

Thanks...
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Answer 2

12⁴ × 9³ × 4

6³ × 8² × 27

= (2²×3)⁴ × (3²)³ × 2²

(2×3)³× (2³)² × 3³

= (2²)⁴ × (3)⁴ × 3²*³ × 2²

2³ × 3³ × 2²*³ × 3³

= 2⁸ × 2² × 3⁴ × 3⁶

2³ × 2⁶ × 3³ × 3³

= 2⁸+² × 3⁴+⁶

2³+⁶ × 3³+³

= 2¹⁰ × 3¹⁰

2⁹ × 3⁶

= 2¹⁰-⁹ × 3¹⁰-⁶

= 2¹ × 3⁴

= 2 × 3⁴