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4^((1)/(5))*3^((2)/(5))=y^((1)/(5)) What value of y satisfies the given equation?

415⋅325=y15 4^{\frac{1}{5}} \cdot 3^{\frac{2}{5}}=y^{\frac{1}{5}} \newlineWhat value of y y satisfies the given equation?

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Full solution

Q. 415⋅325=y15 4^{\frac{1}{5}} \cdot 3^{\frac{2}{5}}=y^{\frac{1}{5}} \newlineWhat value of y y satisfies the given equation?
  1. Write equation: Write down the given equation.\newlineThe given equation is 415⋅325=y154^{\frac{1}{5}} \cdot 3^{\frac{2}{5}} = y^{\frac{1}{5}}.
  2. Raise to power of 55: Raise both sides of the equation to the power of 55 to eliminate the fifth root.(415⋅325)5=(y15)5(4^{\frac{1}{5}} \cdot 3^{\frac{2}{5}})^5 = (y^{\frac{1}{5}})^5
  3. Apply power of a power rule: Apply the power of a power rule to simplify both sides.\newline4(1/5⋅5)⋅3(2/5⋅5)=y(1/5⋅5)4^{(1/5 \cdot 5)} \cdot 3^{(2/5 \cdot 5)} = y^{(1/5 \cdot 5)}
  4. Simplify exponents: Simplify the exponents. 41×32=y14^1 \times 3^2 = y^1
  5. Calculate left side: Calculate the left side of the equation.\newline4×32=4×9=364 \times 3^2 = 4 \times 9 = 36
  6. Write simplified equation: Write down the simplified equation. 36=y36 = y

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