The equivalent expression is (7/4)² x (2/3)³
Option B is the correct answer.
Given,
[(4/7)^2 x (2/3)^-3]^-1
We need to see which option is correct.
What is the law of exponents with integer exponents?
Here the exponents are the power of a given number where the power is an integer.
Example:
3^a
where a can be -1,-2,-4,-5, 3, 4, 5.
(1/3)^-a = 1^-a / 3^-a = 1 / 3^-a = 1/ (1/3^a) = 3^a
We have,
[(4/7)^2 x (2/3)^-3]^-1
Removing the second bracket.
(4/7)^(2x-1) x (2/3)^-3x(-1)
(4/7)^-2 x (2/3)^3
We can write,
(4/7)^-2
= 1/(4/7)^2
= (7/4)^2
(4/7)^-2 x (2/3)^3
= (7/4)^2 x (2/3)^3
Thus the equivalent expression is (7/4)² x (2/3)³
Option B is the correct answer.
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