Question

(-4/7)³×(5/8)²×(21/5)³ Solve it​

Answer 1

Question

Solve ⇒ $\sf (\frac{-4}{7})^{3}\times (\frac{5}{8})^{2} \times (\frac{21}{5})^{3}$

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Answer

First of all, we'll apply this law of exponent ⇒ $a^{m}\times b^{m} = (ab)^{m}$

⇒ $\sf (\frac{-4}{7})^{3}\times (\frac{5}{8})^{2} \times (\frac{21}{5})^{3}$

⇒ $\sf (\frac{-4}{7} \times \frac{21}{5} )^{3}\times (\frac{5}{8})^{2}$

⇒ $\sf (\frac{-4}{7\div 7 } \times \frac{21\div 7 }{5} )^{3}\times (\frac{5}{8})^{2}$

⇒ $\sf (\frac{-4}{1} \times \frac{3}{5} )^{3}\times (\frac{5}{8})^{2}$

⇒ $\sf (\frac{-12}{5} )^{3}\times (\frac{5}{8})^{2}$

Now we will give the actual value of this rational numbers and solve.

⇒ $\sf (\frac{-12}{5} )^{3}\times (\frac{5}{8})^{2}$

⇒ $\sf \frac{-1728}{125} \times \frac{25}{64}$

⇒ $\sf \frac{-1728\div 64 }{125 \div 25 } \times \frac{25\div 25 }{64\div 64 }$

⇒ $\sf \frac{-27}{5 } \times \frac{1 }{1 }$

⇒ $\sf \frac{-27}{5}$

$\bf \therefore (\frac{-4}{7})^{3}\times (\frac{5}{8})^{2} \times (\frac{21}{5})^{3} = \frac{-27}{5}$

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Answer 2

$\huge\sf { _!! Question !_! }$

$\rm\red { \huge{ ( } \small{ \dfrac{ - 4}{7}\huge) }^{3} \times \huge{ ( } \small{ \dfrac{ 5}{8}\huge) }^{2} \times \huge{ ( } \small{ \dfrac{ 21}{5}\huge) }^{3} }$

$\huge\sf { _!! Solution !_! }$

$\sf { \qquad \longrightarrow \huge{ ( } \small{ \dfrac{ - 4}{7}\huge) }^{3} \times \huge{ ( } \small{ \dfrac{ 5}{8}\huge) }^{2} \times \huge{ ( } \small{ \dfrac{ 21}{5}\huge) }^{3} }$

$\sf { \qquad \longrightarrow \huge{ ( } \small{ \dfrac{ - 4}{ \cancel 7} \times \dfrac{ {\cancel{ 21}}^{ \: \: 3} }{5}\huge) }^{3} \times \huge{ ( } \small{ \dfrac{ 5}{8}\huge) }^{2} }$

[ Since $\rm { {x}^{n} \times { y}^{n} = {(xy)}^{n} }]$

$\sf { \qquad \longrightarrow \huge{ ( } \small{ \dfrac{ -12}{ 5} \huge) }^{3} \times \huge{ ( } \small{ \dfrac{ 5}{8}\huge) }^{2} }$

$\sf { \qquad \longrightarrow \huge{ ( } \small\dfrac{ \cancel{ -1728} {}^{ \: \: - 432} } {\cancel{ 125} {}^{ \: \: 5} } \huge) \times \huge{ ( } \small \dfrac{\cancel{ 25}{ }^{ \: \: 1} }{\cancel{ 64} {}^{ \: \:16 } }\huge) }$

$\sf { \qquad \longrightarrow \huge{ ( } \small \dfrac{\cancel{-432}{}^{ \: \: -27}}{5} \times \dfrac{1}{\cancel{16} {}^{ \: \: 1}} \huge) }$

$\sf\blue { \qquad \longrightarrow \huge{ ( } \small \dfrac{-27}{5} ( Ans)\huge) }$

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$\huge\sf { _!! Additionally !_! }$

Laws of exponents:

• $\sf { {x} ^{m} \times {x} ^{n}= {x} ^{m+n}}$

• $\sf { {({x} ^ {m})} ^{n} = {x} ^{mn}}$

• $\sf { {(xy) } ^{m} = {x} ^{m} {y} ^{m} }$

• $\sf {{(\dfrac{x}{y})} ^{m} = \dfrac{{x} ^{m}} {{y} ^{m}}}$ [Where, y ≠ 0.]

• $\sf{ {x} ^{m} ÷{x} ^{n} = {x} ^{m-n}}$

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