Calculating the Value of y
<p>Given \( y^2 = 125^{\frac{2}{3}} \times 343^{\frac{2}{3}} \).</p>
<p>We can simplify this as:</p>
<p> \( y^2 = (125 \times 343)^{\frac{2}{3}} \).</p>
<p>Now calculate \( 125 \) and \( 343 \):</p>
<p> \( 125 = 5^3 \) and \( 343 = 7^3 \). </p>
<p>Thus, \( 125 \times 343 = 5^3 \times 7^3 = (5 \times 7)^3 = 35^3 \).</p>
<p>Substituting back, we have \( y^2 = (35^3)^{\frac{2}{3}} = 35^{2} \).</p>
<p>So, \( y = \sqrt{35^{2}} = 35 \).</p>
<p>Therefore, the value of \( y \) is:</p>
<p> \( y = 35 \).</p>
