Simplify and give reasons(4/7)^-5×(7/4)^-7
Answers
Answered by
2
Step-by-step explanation:
Answer:
(\frac{4}{7})^{2}(
7
4
)
2
Step-by-step explanation:
Given : (\frac{4}{7})^{-5} \times (\frac{7}{4})^{-7}(
7
4
)
−5
×(
4
7
)
−7
To Find : Simplify
Solution:
(\frac{4}{7})^{-5} \times (\frac{7}{4})^{-7}(
7
4
)
−5
×(
4
7
)
−7
Property: a^{-x}=(\frac{1}{a})^x[/tex So, [tex](\frac{4}{7})^{-5} \times (\frac{4}{7})^{7}a
−x
=(
a
1
)
x
[/texSo, [tex](
7
4
)
−5
×(
7
4
)
7
Property: a^x \times a^y = a^{x+y}a
x
×a
y
=a
x+y
So, (\frac{4}{7})^{-5+7}(
7
4
)
−5+7
(\frac{4}{7})^{2}(
7
4
)
2
Hence (\frac{4}{7})^{-5} \times (\frac{7}{4})^{-7}(
7
4
)
−5
×(
4
7
)
−7
= (\frac{4}{7})^{2}(
7
4
)
2
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