Simplify the following and write in exponential form.(3^6 ÷ 3^8) ×3^-4
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0
Answer:
(3
6
÷3
8
)
4
×3
−4
= \Big(\frac{3^{6}}{3^{8}}\Big)^{4} \times \frac{1}{3^{4}}=(
3
8
3
6
)
4
×
3
4
1
= \Big(\frac{1}{3^{8-6}}\Big)^{4} \times \frac{1}{3^{4}}=(
3
8−6
1
)
4
×
3
4
1
\boxed{ \pink{ \frac{a^{m}}{a^{n}} = \frac{1}{a^{n-m}} }}
a
n
a
m
=
a
n−m
1
= \frac{1}{(3^{2})^{4}} \times \frac{1}{3^{4}}=
(3
2
)
4
1
×
3
4
1
= \frac{1}{3^{2\times 4 } \times 3^{4}}=
3
2×4
×3
4
1
= \frac{1}{3^{8+4}}=
3
8+4
1
= \frac{1}{3^{12}}=
3
12
1
Therefore.,
\red{(3^{6} \div 3^{8})^4 \times 3^{-4}}(3
6
÷3
8
)
4
×3
−4
\green { = \frac{1}{3^{12}}}=
3
12
1
Step-by-step explanation:
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