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Sergeu [11.5K]
3 years ago
12

13.......................

Mathematics
1 answer:
Alla [95]3 years ago
5 0

Answer:

The answer is (d) ⇒ pq^{2}r\sqrt[3]{pr^{2}}

Step-by-step explanation:

* To simplify the cube roots:

 If its number then the number must be written in the form x³

 then we divide the power by 3 to cancel the radical

 If its variable we divide its power by 3 to cancel the radical

∵ \sqrt[3]{p^{4}q^{6}r^{5}}=p^{\frac{4}{3}}q^{\frac{6}{3}}r^{\frac{5}{3}}}

∴ p^{\frac{4}{3}}q^{2}}r^{\frac{5}{3}}=p^{1\frac{1}{3}}q^{2}r^{1\frac{2}{3}}

∵ p^{\frac{1}{3}}=\sqrt[3]{p}

∵ r^{\frac{2}{3}}=\sqrt[3]{r^{2}}

∴ p(p)^{\frac{1}{3}}q^{2}r(r)^{\frac{2}{3}}=p(\sqrt[3]{p})q^{2}r(\sqrt[3]{r^{2}})

∴ prq^{2}\sqrt[3]{pr^{2}}}

∴ The answer is (d)

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