Question

Simplify and write your solution.

1. (m¹⁶n²⁸o²)^½,
2. (m)²/⁴
3. 6(xm)⁴/³

Answer 1

The given expressions are simplified using rules of exponents. Expression 1 becomes m⁸ n⁾ o¹, Expression 2 becomes m¹⁄₂, and Expression 3 becomes 216x⁹m⁹.

Step-by-step explanation:

For simplifying the given expressions, we apply the rules of exponents and scientific notation.

1. (m¹⁶n²⁸o²)^½: When you take the square root of an expression (which is what raising to the ½ power is), you divide the exponents by 2. Thus, m⁸ n⁺ o¹.
2. (m)²/⁴: To raise a term to a fractional power, you multiply the exponents. Here it would simplify to mⁱ since 2 times ⁴ is ½.
3. For 6(xm)⁴/³, you cube the coefficient (6), which is 216, and multiply the exponents of the variables inside the parenthesis by ³, so the result is 216xₓmₓ.

Cubing of exponentials involves cubing the digit and multiplying the exponent by 3 as demonstrated in part 3. Scientific notation is used when expressing very large or very small numbers in terms of a power of ten, as shown in various examples provided.