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6 votes
Find the value of (8/125)^-2/3

User Yitzih
by
7.0k points

1 Answer

8 votes

Answer:

6.25

Explanation:

Using the rules of exponents


((a)/(b)) ^{-(m)/(n) } =
((b)/(a)) ^{(m)/(n) }


a^{(m)/(n) } =
(\sqrt[n]{a} )^m

Given


((8)/(125)) ^{-(2)/(3) }

=
((125)/(8)) ^{(2)/(3) }

=
(\sqrt[3]{125} )^2 ×
\frac{1}{(\sqrt[3]{8})^2 }

= 5² ×
(1)/(2^2)

= 25 ×
(1)/(4)

=
(25)/(4)

= 6.25

User Vlad Macovei
by
8.0k points