Question

simplify plz plz help​

Answer 1

Simplify :

$\sf \bigg( 32 \times {a}^{10} \times {b}^{ - 5} \bigg)^{ \frac{1}{5} }$

Identity used :

$\sf \bullet \: {( {p}^{m} )}^{n} \: = \: {p}^{(m \times n)} \\ \\ \sf \bullet \: {p}^{( - m) \: = \: } \bigg( \dfrac{1}{p} \bigg)^{m} \\ \\ \sf \bullet \: {( {p} \times q \times r)}^{n} \: = \: {p}^{n} \times {q}^{n} \times {r}^{n}$

Solution :

$\sf \bigg( 32 \times {a}^{10} \times {b}^{ - 5} \bigg)^{ \frac{1}{5} } \\ \\ \sf \implies \: \bigg( (2 \times 2 \times 2 \times 2 \times 2)\times {a}^{10} \times {b}^{ - 5} \bigg)^{ \frac{1}{5} } \\ \\ \sf \implies \: \bigg( ( {2}^{5} )\times {a}^{10} \times {b}^{ - 5} \bigg)^{ \frac{1}{5} } \\ \\ \sf \implies \: {2}^{(5 \times \frac{1}{5} )} \times {a}^{(10 \times \frac{1}{5}) } \times {b}^{( - 5 \times \frac{1}{5} )} \\ \\ \sf \implies \: 2 \times {a}^{2} \times {b}^{ - 1} \\ \\ \sf \implies \: 2 \times {a}^{2} \times \dfrac{1}{b} \\ \\ \sf \implies \: \dfrac{2 {a}^{2} }{b}$

ANSWER : 2a² ÷ b