Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers. The expression which is equal to the given expression is,
![\dfrac{1}{(r)^{42}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%28r%29%5E%7B42%7D%7D%20)
The option B is the correct option.
Given information-
The given expression in the problem is,
![[(r)^{-7}]^5](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E5)
<h3>Power rule of exponents</h3>
Power rule of exponents says that the power of the power of a exponent is equal to the multiplying both the powers.
Suppose<em> </em><em>x</em> is a number with power <em>a. </em>The power is power of the power of number <em>x. </em>Then by the power rule of the exponents,
![(x^a)^b=x^{ab}](https://tex.z-dn.net/?f=%28x%5Ea%29%5Eb%3Dx%5E%7Bab%7D)
Using the power rule of the exponents given expression can be written as,
![[(r)^{-7}]^6=(r)^{-7\times 6} ](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E6%3D%28r%29%5E%7B-7%5Ctimes%206%7D%20%0A)
![[(r)^{-7}]^6=(r)^{-42}](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E6%3D%28r%29%5E%7B-42%7D)
<h3>Negative exponents rule</h3>
Negative exponents rule says that when a power of a number is negative, then write the number in the denominator with the same power with positive sign.Thus,
![[(r)^{-7}]^6=\dfrac{1}{(r)^{42}}](https://tex.z-dn.net/?f=%5B%28r%29%5E%7B-7%7D%5D%5E6%3D%5Cdfrac%7B1%7D%7B%28r%29%5E%7B42%7D%7D%20)
Hence the expression which is equal to the given expression is,
![\dfrac{1}{(r)^{42}}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%28r%29%5E%7B42%7D%7D%20)
The option B is the correct option.
Learn more about the power rule of exponents here;
brainly.com/question/819893