Final answer:
The evaluation of the expression 64¹⁄² x 10⁻² results in the fraction 2/25 when expressed in its simplest form. This is achieved by taking the square root of 64, which is 8, and multiplying by 10⁻², which equals 1/100. The final answer is obtained by simplifying 8/100 to 2/25.
Step-by-step explanation:
The question asks to evaluate 64¹⁄² x 10⁻² and express the answer as a fraction in its simplest form. Let's break down the given expression.
The expression 64¹⁄² means the square root of 64. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, since 8 x 8 = 64, the square root of 64 is 8. Hence, 64¹⁄² = 8.
Next, we evaluate 10⁻². A negative exponent indicates that we inverse the number (make it a fraction) and the exponent positive. Therefore, 10⁻² is equivalent to 1/10² or 1/100.
Now, we multiply the two results together: 8 x 1/100 = 8/100. Simplifying the fraction by dividing both numerator and denominator by 4 gives us 2/25 which is the simplest form.
In summary, the expression 64¹⁄² x 10⁻² evaluated and expressed as a fraction in its simplest form is 2/25.