simplyfy the laws of exponents
Answers
Answer:
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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
Answer:
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