Answer:
![\dfrac{b^6}{64}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bb%5E6%7D%7B64%7D%20)
Step-by-step explanation:
We need three rules. Raising a power to a power. Raising a product to a power. Raising a number to a negative exponent.
Rule 1:
To raise a power to a power, multiply powers.
![(a^m)^n = a^{mn}](https://tex.z-dn.net/?f=%20%28a%5Em%29%5En%20%3D%20a%5E%7Bmn%7D%20)
Rule 2:
To raise a product to a power, raise every factor of the product to the power.
![(a^xb^yc^z)^n = a^{xn}b^{yn}c^{zn}](https://tex.z-dn.net/?f=%20%28a%5Exb%5Eyc%5Ez%29%5En%20%3D%20a%5E%7Bxn%7Db%5E%7Byn%7Dc%5E%7Bzn%7D%20)
Rule 3:
To raise a number to a negative power, follow this formula.
![a^{-n} = \dfrac{1}{a^n}](https://tex.z-dn.net/?f=%20a%5E%7B-n%7D%20%3D%20%5Cdfrac%7B1%7D%7Ba%5En%7D%20)
Your problem.
![(2^2b^{-2})^{-3} =](https://tex.z-dn.net/?f=%20%282%5E2b%5E%7B-2%7D%29%5E%7B-3%7D%20%3D%20)
You have a product raised to a power, so raise each factor to the power.
![= (2^2)^{-3}(b^{-2})^{-3}](https://tex.z-dn.net/?f=%20%3D%20%282%5E2%29%5E%7B-3%7D%28b%5E%7B-2%7D%29%5E%7B-3%7D%20)
Now raise each power to a power by multiplying exponents.
![= 2^{2 \times (-3)}b^{-2 \times (-3)}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B2%20%5Ctimes%20%28-3%29%7Db%5E%7B-2%20%5Ctimes%20%28-3%29%7D%20)
![= 2^{-6}b^{6}](https://tex.z-dn.net/?f=%20%3D%202%5E%7B-6%7Db%5E%7B6%7D%20)
Now we follow the rule of a negative exponent.
![= \dfrac{1}{2^6} \times b^6](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7B1%7D%7B2%5E6%7D%20%5Ctimes%20b%5E6%20)
![= \dfrac{b^6}{2^6}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7Bb%5E6%7D%7B2%5E6%7D%20)
![= \dfrac{b^6}{2 \times 2 \times 2 \times 2 \times 2 \times 2}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7Bb%5E6%7D%7B2%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%20%5Ctimes%202%7D%20)
![= \dfrac{b^6}{64}](https://tex.z-dn.net/?f=%20%3D%20%5Cdfrac%7Bb%5E6%7D%7B64%7D%20)
Answer: ![\dfrac{b^6}{64}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bb%5E6%7D%7B64%7D%20)