Question

refer to the attachment and answer correctly​

Answer 1

⟹$\dfrac{\sqrt[4]{1250} }{ \sqrt[4]{2} }$

⟹$\dfrac{ {(1250)}^{ \frac{1}{4} } }{ {(2)}^{ \frac{1}{4} } }$

⟹${ (\dfrac{1250}{2}) }^{ \frac{1}{4} }$

Now , 625×2 = 1250

⟹${ (625) }^{ \frac{1}{4} }$

we know :- 625= 5×5×5×5 = 5⁴

⟹${ (5 \times 5 \times 5 \times 5) }^{ \frac{1}{4} }$

⟹${( {5}^{4} )}^{ \frac{1}{4} }$

⟹${( 5) }^{ \frac{1}{4} \times 4}$

⟹$5$

Answer :- 5

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Laws of exponent :-

$1)a^m \times a^n= {a}^{(m + n)}$

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

$3) {ab}^{n} = {a}^{n} {b}^{n}$

$4) \frac{ {(a)}^{m} }{ {(a)}^{n} } = {a}^{m - n}$

$5) {a}^{ - b} = \frac{1}{ {a}^{b} }$

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