Final answer:
To evaluate 5⁻² x 3 √8, we first simplify 5⁻² to 1/25, and find that 3 √8 is equivalent to 6√2. Multiplying these together yields the answer 6√2/25.
Step-by-step explanation:
To solve the mathematical expression 5⁻² x 3 √8, we first address each part of the expression individually.
The term 5⁻² is the same as 1/5², which simplifies to 1/25. Next, the term 3 √8 involves finding the square root of 8, and then multiplying the result by 3.
The square root of 8 is 2√2, hence 3 √8 simplifies to 3 x 2√2, or 6√2.
Multiplying these two simplified expressions, 1/25 x 6√2, gives us 6√2/25, which is the final simplified form of the original expression.