Question

simplify 12 4 × 9 3 × 4/ 6 3 × 8 2 × 27
pls help ​

Answer 1

Step-by-step explanation:

Hey friend,

Here is the answer you were looking for:

\begin{gathered} \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} \end{gathered}

6

3

×8

2

×27

12

4

×9

3

×4

=

2

3

×3

3

×2

2

×2

2

×2

2

×3

3

3

4

×2

4

×2

4

×3

3

×3

3

×2

2

usingtheidentity

a

m

×a

n

=a

m+n

=

2

3+2+2+2

×3

3+3

2

4+4+2

×3

4+3+3

=

2

9

×3

6

2

10

×3

10

usingtheidentity

a

n

a

m

=a

m−n

=2

10−9

×3

10−6

=2

1

×3

4

=2×3

4

Hope this helps!!!

@Mahak24

Thanks...

☺☺