Final answer:
The expression (2ᵀ⁴/8ᵀ⁴)² simplifies by subtracting exponents to 2-2ᵀ⁴, then squaring the result to 2-4ᵀ, and finally, using the reciprocal to rewrite it with a positive exponent as 24ᵀ.
Step-by-step explanation:
The expression given is (2ᵀ⁴/8ᵀ⁴)². To simplify this, we will first simplify the expression inside the parentheses before squaring. We know that 8 is equivalent to 23, so 8ᵀ⁴ can be written as (23)ᵀ⁴ which equals 23ᵀ⁴. Thus, we can simplify the initial fraction to 2ᵀ⁴ / 23ᵀ⁴.
To divide expressions with the same base, we subtract the exponents: ᵀ⁴ - (3ᵀ) = -2ᵀ⁴. So the expression simplifies to 2-2ᵀ⁴.
When we square a power, we multiply the exponent by 2, which in this case gives us 2-2ᵀ· 2 = 2-4ᵀ. Lastly, to express the answer with positive exponents, we take the reciprocal of the base which finally gives us the simplified expression 24ᵀ.