To solve the equation \( x^3 = y^4 \) for \( y \) given that \( x = 15 \), we start by substituting \( x \) into the equation:
\[ 15^3 = y^4 \]
Calculating \( 15^3 \):
\[ 15^3 = 15 \times 15 \times 15 = 225 \times 15 = 3375 \]
Now we have:
\[ 3375 = y^4 \]
To find \( y \), we take the fourth root of both sides:
\[ y = \sqrt[4]{3375} \]
To simplify \( \sqrt[4]{3375} \), we can factor \( 3375 \):
\[ 3375 = 3^3 \times 5^3 \]
Now, taking the fourth root:
\[ y = \sqrt[4]{3^3 \times 5^3} = \sqrt[4]{(3 \times 5)^3} = \sqrt[4]{15^3} \]
This can be expressed as:
\[ y = 15^{3/4} \]
To compute \( 15^{3/4} \):
- Calculate \( 15^{3/4} \) using exponentiation: \[ 15^{3/4} = (15^3)^{1/4} = \sqrt[4]{3375} \approx 8.16 \]
Using a calculator or exponent simplification gives:
\[ y \approx 11.18 \]
Therefore, the approximate value of \( y \) is:
\[ \boxed{11.18} \text{ units} \]
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