Question

Solve for m:-

${ \frac{2}{5} }^{-3} + { \frac{2}{5} }^{m} = { \frac{2}{5} }^{5}$
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Answer 1

Answer:

$\boxed{\sf\ \implies:m = 8 }$

Step-by-step explanation:

${ \frac{2}{5} }^{-3} + { \frac{2}{5} }^{m} = { \frac{2}{5} }^{5} \\ \\ \sf\ \implies: - 3 + m = 5 \\ \\ \sf\ \implies:m = 5 + 3 \\ \\ \boxed{\sf\ \implies:m = 8 } </p><p>$

Answer 2

Question:-

Solve for m:-

$({ \frac{2}{5} })^{ - 3} + ( { \frac{2}{5} })^{m} = ( { \frac{2}{5} })^{5}$

${\green{\underline{\underline{\bold{Solution:-}}}}}$

$({ \frac{2}{5} })^{ - 3} + ( { \frac{2}{5} })^{m} = ( { \frac{2}{5} })^{5}$

As we know $({a})^{-n} = \frac{1}{{a}^{n}}$

$({ \frac{2}{5} })^{ - 3} = ({ \frac{5}{3} })^{ 3}$

$({ \frac{5}{3} })^{ 3} + ({ \frac{2}{5} })^{m} = ({ \frac{2}{5} })^{5}$

$({ \frac{2}{5} })^{ m} = ({ \frac{2}{5} })^{5} = ({ \frac{2}{5} })^{3}$

$({ \frac{2}{5} })^{m} = ({ \frac{2}{5} })^{5+3}$ [ Since, ${a}^{m}×{a}^{n} = {a}^{m+n}$ ]

$({ \frac{2}{5} })^{m} = ({ \frac{2}{5} })^{8}$

m = 8 [ If ${a}^{m}={a}^{n} ,\:then\: m = n$ ]

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Identities used here:-

• $({a})^{-n} = \frac{1}{{a}^{n}}$
• ${a}^{m}×{a}^{n} = {a}^{m+n}$
• If ${a}^{m}={a}^{n} ,\:then\: m = n$