MCQ
Simplified value of $(25)^{\frac{1}{3}}\times(5)^{\frac{1}{3}}$ is:
- A$25$
- B$3$
- C$1$
- ✓$5$
✓
Answer
Correct option: D.
$5$
$(25)^{\frac{1}{3}}\times(5)^{\frac{1}{3}}$
$\Rightarrow(25\times3)^{\frac{1}{3}}...$
$[\therefore\text{m}^\text{x}\times\text{n}^\text{x}=(\text{m}\times\text{n})^\text{x}]$
$\Rightarrow(125)^\frac{1}{3}$
$\Rightarrow\sqrt[3]{125}=5$
$\therefore(25)^{\frac{1}{3}}\times(5)^{\frac{1}{3}}=5$
$\Rightarrow(25\times3)^{\frac{1}{3}}...$
$[\therefore\text{m}^\text{x}\times\text{n}^\text{x}=(\text{m}\times\text{n})^\text{x}]$
$\Rightarrow(125)^\frac{1}{3}$
$\Rightarrow\sqrt[3]{125}=5$
$\therefore(25)^{\frac{1}{3}}\times(5)^{\frac{1}{3}}=5$
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