Rewrite the expression in the form y^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). root(3)((y^(2))/(y^((4)/(5))))=◻

Question

Rewrite the expression in the form  y^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).  root(3)((y^(2))/(y^((4)/(5))))=◻

Bytelearn · Accepted Answer

Rewrite as Exponent: Apply the property of radicals to rewrite the cube root as an exponent. root(3)((y^(2))/(y^((4)/(5)))) = (y^(2))^(1/3) / (y^((4)/(5)))^(1/3)Simplify with Power Rule: Use the power rule of exponents to simplify the expression. (y^(2))^(1/3) becomes y^(2*(1/3)) which simplifies to y^(2/3). (y^((4)/(5)))^(1/3) becomes y^((4/5)*(1/3)) which simplifies to y^(4/15).Divide Using Quotient Rule: Now, divide the two expressions using the quotient rule for exponents. y^(2/3) / y^(4/15)Subtract Exponents: To divide the expressions with the same base, subtract the exponents. y^(2/3 - 4/15)Find Common Denominator: Find a common denominator to subtract the fractions in the exponents. The common denominator for 3 and 15 is 15. y^(10/15 - 4/15)Subtract Fractions: Subtract the fractions in the exponent. y^(10/15 - 4/15) = y^(6/15)Simplify Fraction: Simplify the fraction in the exponent. y^(6/15) simplifies to y^(2/5) because 6 and 15 have a common factor of 3.

Rewrite the expression in the form $y^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $\sqrt[3]{\frac{y^{2}}{y^{\frac{4}{5}}}}=\square$

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Rewrite the expression in the form $y^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $\sqrt[3]{\frac{y^{2}}{y^{\frac{4}{5}}}}=\square$