Final answer:
The expression (8^-1×3^2)^2 simplifies to 81/64 by following the rules of exponents - apply the exponent to each factor inside the parentheses, simplify using base conversion if necessary, and multiply the results.
Step-by-step explanation:
To simplify the expression (8^-1×3^2)^2, we need to follow the rules of exponents. First, we'll apply the exponent to each factor inside the parentheses:
- (8^-1)^2 becomes 8^-2 because we multiply the exponents.
- (3^2)^2 becomes 3^4 for the same reason.
Next, we'll combine these resulting exponents:
8^-2×3^4
Because 8 is 2^3, we can rewrite 8^-2 as (2^3)^-2 which becomes 2^-6 when we multiply the exponents. Now we have:
2^-6×3^4
To simplify this further, we can leave the expression as a product of two terms with negative and positive exponents, respectively:
1/2^6×3^4
Which simplifies to:
1/64Ó81
Now we can multiply these numbers to get the simplified expression:
81/64
So the simplified expression for (8^-1×3^2)^2 is 81/64.