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Write the following as an exponential expression.

root(3)(y^(2))

Write the following as an exponential expression.\newliney23 \sqrt[3]{y^{2}}

Full solution

Q. Write the following as an exponential expression.\newliney23 \sqrt[3]{y^{2}}
  1. Identify Components: Identify the components of the expression.\newlineThe expression is the cube root of yy squared. This involves a radical expression with an index of 33, since it is a cube root, and an exponent of 22, because it is yy squared.
  2. Convert to Exponential: Convert the radical expression to an exponential expression.\newlineThe cube root of a number can be expressed as that number raised to the power of 13\frac{1}{3}. Therefore, the cube root of yy squared is yy squared raised to the power of 13\frac{1}{3}.
  3. Apply Power Rule: Apply the power to a power rule.\newlineWhen you raise a power to another power, you multiply the exponents. In this case, y2y^2 raised to the power of 13\frac{1}{3} is y2×13y^{2 \times \frac{1}{3}}.
  4. Perform Exponent Multiplication: Perform the multiplication of the exponents.\newlineMultiply 22 by 1/31/3 to get 2/32/3. So, yy squared raised to the power of 1/31/3 is y2/3y^{2/3}.