Question

Solve for m:

(-5)^m-1 / (-5)^2 = (-5)^-8​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

GIVEN :-

• $\rm{( - 5) ^{m - 1} } \: \div ( - 5) = ( - 5) ^{ - 8}$

TO FIND :-

• $\rm{ value \: of \: m \: }$

SOLUTION :-

$\implies \: \rm{( - 5) ^{m - 1} } \: \div ( - 5) = ( - 5) ^{ - 8}$

$\implies\rm{ \dfrac{( - 5) ^{m - 1}} {( - 5) ^{2} \: \: \: \: } = ( - 5) ^{ - 8}}$

$\implies$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \boxed{ { \frac{ {a}^{m} }{ {a}^{n} } \: = \: a ^{m - n} }}}$

$\implies \rm{ ({ - 5})^{m - 1 - 2} } = ( - {5})^{ - 8}$

$\implies \rm{ ({ - 5})^{m - 3} } = ( - {5})^{ - 8}$

$\implies \rm{ m \: - 3 = - 8}$

$\implies \boxed{ \boxed { \rm { m \: = -5}}}$

OTHER INFORMATION

Basic formulas in Powers and Roots

Some basic formulas used to solve questions on exponents are

(am)n = (an)m = amn

am.an = am+n

a-m = 1/am

am/an = am-n = 1/an-m

(ab)n = anbn

(a/b)n = an/bn

aⁿ = 1 ( where n = 0 )