Question

Apply the power of a power property to simplify the expression: y⁴/³ . y ⁻¹/² = y²⁻¹/² =

Answer 1

Apply the power of a power property to simplify y⁴/³ · y⁻¹/² by adding the exponents to get y⁵/⁶. Negative exponents represent division, while expressions with fractional exponents denote roots.

Step-by-step explanation:

To apply the power of a power property and simplify the expression y⁴/³ · y⁻¹/², we use the rule that states we should add the exponents when multiplying two powers with the same base. In this case, the base is y, and the exponents are 4/3 and -1/2. Adding these exponents:

• (4/3) + (-1/2) = (8/6) - (3/6) = 5/6

So, the simplified expression is y⁵/⁶.

Negative exponents denote the inverse operation, where x⁻¹ is equivalent to 1/x. For example, 3⁻⁴ equals 1/3³³³³, which demonstrates division instead of multiplication. Similarly, when simplifying expressions with fractional exponents, remember that an expression such as x² represents the square root, or √x, and that the power inside the parentheses affects everything, just as in (27x³)(4x²) = 2.1 × 10⁻³³.

The complete question is:Apply the power of a power property to simplify the expression: y⁴/³ . y ⁻¹/² = y²⁻¹/² =is: