Question

what is (-4 by 7)power 3×(5 by 8)power 2×(21 by 5)power 3​

Answer 1

$\huge\sf {Solution}$

$\sf { \qquad \longrightarrow \huge{ ( } \small{ \dfrac{ - 4}{7}\huge) }^{3} \times \huge{ ( } \small{ \dfrac{ 5}{8}\huge) }^{2} \times \huge{ ( } \small{ \dfrac{ 21}{5}\huge) }^{3} }⟶(7−4)3×(85)2×(521)3</p><p>\sf { \qquad \longrightarrow \huge{ ( } \small{ \dfrac{ - 4}{ \cancel 7} \times \dfrac{ {\cancel{ 21}}^{ \: \: 3} }{5}\huge) }^{3} \times \huge{ ( } \small{ \dfrac{ 5}{8}\huge) }^{2} }[ Since \rm { {x}^{n} \times { y}^{n} = {(xy)}^{n} }]xn×yn=(xy)n]$

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

$\sf { \qquad \longrightarrow \huge{ ( } \small\dfrac{ \cancel{ -1728} {}^{ \: \: - 432} } {\cancel{ 125} {}^{ \: \: 5} } \huge) \times \huge{ ( } \small \dfrac{\cancel{ 25}{ }^{ \: \: 1} }{\cancel{ 64} {}^{ \: \:16 } }\huge) }⟶(1255−1728−432)×(6416251)$

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

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

_____________________________

$\huge\sf {Additionally}$

Laws of exponents:

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

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

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

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

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

Answer 2

Step-by-step explanation:

(−4)5÷(−4)8

=(−4)8(−4)5=(−4)5−8

=(−4)−3=((−4)3)−1

=(−64)−1

=64−1

=26−1