Question

12⁴×9³×4/6³×8²×2raise to the power 7 PLEASE I WILL MARK AS BRAINLIEST​

Answer 1

Answer: 3^7

Step-by-step explanation:

(12)^4 = (4×3)^4=4^4×3^4=2^8×3^4

(9)³=(3²)³=(3)^6

4=2²

6³=(3×2)³=3³×2³

8²=(2³)²=2^6

2=2^1

Now,

2^8×3^4×3^6×2²/3³×2³×2^6×2^1

2^8×3^4×3^6×2²×3^-3×2^-3×2^-6×2^-1

2°×3^7

3^7

so, Mark me brainliest

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: ANSWER \: \: } \mid}}}}}$

$\: \: \: \: \: \mathtt{\frac{12 {}^{4} \times 9 {}^{3} \times 4 }{6 {}^{3} \times 8 {}^{2} \times 2 } } \\ \\ \mathtt{= \frac{(4 \times 3) {}^{4} \times (3 {}^{2} ) {}^{3} \times (2) {}^{2} }{(2 \times 3) {}^{3} \times (2 {}^{3} ) {}^{2} \times 2} } \\ \\ \mathtt{= \frac{(4) {}^{4} \times (3) {}^{4} \times (3) {}^{6} \times (2) {}^{2} }{(2) {}^{3} \times (3) {}^{3} \times (2) {}^{6} \times 2 } }\\ \\ \mathtt{= \frac{(2{}^{2} ) {}^{4} \times (3) {}^{4} \times (3) {}^{6} \times (2) {}^{2} }{(2) {}^{3} \times (3) {}^{3} \times (2) {}^{6} \times 2} }\\ \\ \mathtt{ = \frac{(2 ) {}^{8} \times (3) {}^{4} \times (3) {}^{6} \times (2) {}^{2} }{(2) {}^{3} \times (3) {}^{3} \times (2) {}^{6} \times 2}} \\ \\ \mathtt{ = \frac{(2) {}^{8} \times (2) {}^{2} \times (3) {}^{4} \times (3) {}^{6} }{2 \times (2) {}^{3} \times (2) {}^{6} \times (3) {}^{3} }} \\ \\ \mathtt{= \frac{ \{(2) {}^{8 + 2} \} \times \{(3) {}^{4 + 6 } \}}{ \{(2) {}^{1 + 3 + 6 } \} \times (3) {}^{3} } } \\ \\ \mathtt{= \frac{ \cancel{(2) {}^{10} }\times (3 ){}^{10} }{ \cancel{(2) {}^{10} }\times (3) {}^{3} }} \\ \\ \mathtt{ = \frac{(3) {}^{10} }{(3) {}^{3} }} \\ \\ \mathtt{= 3 {}^{ 10 - 3} } \\ \\ \mathtt{= 3 {}^{7}} \\ \\ \mathtt{= 2187}$

$\underline{ \underline{ \mathcal{ \red{ : \star : \: IDENTITIES \: \: \: USED \: : \star : }}}} \\ \\ \mathsf{1. \: (a \times b) {}^{m} = a {}^{m} \times b{}^{n} } \\ \\ \mathsf{2. \: (a {}^{m} ) {}^{n} = a {}^{mn} } \\ \\ \mathsf{3. \: a {}^{m} \times a {}^{n} = a {}^{ m+ n} } \\ \\ \mathsf{4. \: \frac{a {}^{m} }{a {}^{n} } = a {}^{m - n} }$