Question:
Simplified value oi $(25)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$ is
(a) 25
(b) 3
(c) 1
(d) 5
Solution:
$(25)^{\frac{1}{2}} \times 5^{\frac{1}{3}}=\left(5^{2}\right)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$
$=5^{\frac{2}{3}} \times 5^{\frac{1}{3}}$
$=5^{\frac{2}{3}+\frac{1}{3}}$
$=5^{\frac{2+1}{3}}$
$=5^{\frac{3}{3}}$
$=5$
$\therefore$ Simplified value of $(25)^{\frac{1}{3}} \times 5^{\frac{1}{3}}$ is $5 .$
Hence, the correct option is (d).
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