Question

(2^2b^-2)^-3
Math help plz

Answer 1

`(b^6)/(64)`

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)`

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)`

Rule 3:

To raise a number to a negative power, follow this formula.

`a^(-n) = (1)/(a^n)`

Your problem.

`(2^2b^(-2))^(-3) =`

You have a product raised to a power, so raise each factor to the power.

`= (2^2)^(-3)(b^(-2))^(-3)`

Now raise each power to a power by multiplying exponents.

`= 2^(2 * (-3))b^(-2 * (-3))`

`= 2^(-6)b^(6)`

Now we follow the rule of a negative exponent.

`= (1)/(2^6) * b^6`

`= (b^6)/(2^6)`

`= (b^6)/(2 * 2 * 2 * 2 * 2 * 2)`

`= (b^6)/(64)`

Answer:
`(b^6)/(64)`