Answer:
[tex] \dfrac{b^6}{64} [/tex]
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.
[tex] (a^m)^n = a^{mn} [/tex]
Rule 2:
To raise a product to a power, raise every factor of the product to the power.
[tex] (a^xb^yc^z)^n = a^{xn}b^{yn}c^{zn} [/tex]
Rule 3:
To raise a number to a negative power, follow this formula.
[tex] a^{-n} = \dfrac{1}{a^n} [/tex]
Your problem.
[tex] (2^2b^{-2})^{-3} = [/tex]
You have a product raised to a power, so raise each factor to the power.
[tex] = (2^2)^{-3}(b^{-2})^{-3} [/tex]
Now raise each power to a power by multiplying exponents.
[tex] = 2^{2 \times (-3)}b^{-2 \times (-3)} [/tex]
[tex] = 2^{-6}b^{6} [/tex]
Now we follow the rule of a negative exponent.
[tex] = \dfrac{1}{2^6} \times b^6 [/tex]
[tex] = \dfrac{b^6}{2^6} [/tex]
[tex] = \dfrac{b^6}{2 \times 2 \times 2 \times 2 \times 2 \times 2} [/tex]
[tex] = \dfrac{b^6}{64} [/tex]
Answer: [tex] \dfrac{b^6}{64} [/tex]
