Final answer:
To simplify ((b⁻³c⁴)/(b⁻⁶))⁴, divide the exponents to get b³, then raise each term to the power of 4. The final simplified form is b¹²c¹⁶.
Step-by-step explanation:
To simplify the given expression ((b⁻³c⁴)/(b⁻⁶))⁴, we should first apply the rules of exponents to the fraction inside the parentheses. To do this, we divide the numbers and subtract the exponents.
First, we recognize that a negative exponent means that the number is inverted. Therefore, b⁻³ can be rewritten as 1/(b³) and b⁻⁶ as 1/(b⁶). Then, when dividing fractions with the same base, we subtract the exponents: (-3) - (-6) becomes -3 + 6 which equals 3.
Now, the fraction simplifies to (b³c⁴)⁴. Next, we apply the power of 4 to both b³ and c⁴. This implies raising each exponent by 4, resulting in b^{3×4} and c^{4×4}. The simplified form of the original expression is b¹²c¹⁶.