Question

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step by step explanation​

Answer 1

Step-by-step explanation:

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Answer 2

Question :

Evaluate:

$(128) {}^{ \frac{ - 2}{7} } - (625 {}^{ - 3} ) {}^{ \frac{ - 1}{4} } + 14(2401) {}^{ \frac{ - 1}{4} }$

Properties of Exponents:

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

$2) \frac{a {}^{m} }{a {}^{n} } = a {}^{m - n}$

$3)a {}^{m} \times b {}^{m} = (ab) {}^{m}$

$4)a {}^{0} = 1$

Solution :

$(128) {}^{ \frac{ - 2}{7} } - (625 { }^{ - 3} ) {}^{ \frac{ - 1}{4} } + 14(2401) {}^{ \frac{ - 1}{4} }$

$= (2 {}^{7} ) {}^{ \frac{ - 2}{7} } - (5 {}^{4} ) {}^{ - 3 \times \frac{ - 1}{4} } + 14 \times ( 7 {}^{4} ) {}^{ \frac{ -1 }{4} }$

$= 2 {}^{ - 2} - 5 {}^{3} + 14 \times 7 { }^{ - 1}$

$= \frac{1}{2 {}^{2} } - 125 + 14 \times \frac{1}{7}$

$= \frac{1}{4} - 625 + 2$

$= \frac{1 - 125 \times 4 + 2 \times 4}{4}$

$= \frac{1-500+8}{4} = \frac{-491}{4}$

it is the required solution!