Question

kindly tell me with explanation:
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Answer 1

Answer:

Neglecting Bases

then,

-5×12 = 3m-2

-60 = 3m-2

-3m = -2+60

-3m = 58

m = 58/-3 ANS

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Answer 2

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$\huge{\textbf{\textsf{{☆ AN}}{\purple{SW}}{\pink{ER ☆} \: {{}{:}}}}}$

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GIVEN :

$({ \frac{2}{3} })^{ - 5} \times ({ \frac{2}{3} })^{12} = ({ \frac{2}{3} })^{3m - 2}$

CONCEPT :

➳ Exponents and Powers

SOLUTION :

$\large\boxed{ {a}^{m} + {a}^{n} = {a}^{m + n} }$

⟼ By using the formula,

$({ \frac{2}{3} })^{ - 5} \times ({ \frac{2}{3} })^{12} = ({ \frac{2}{3} })^{3m - 2} \\ \\ ({ \frac{2}{3} })^{ - 5 + 12} = ({ \frac{2}{3} })^{3m - 2}$

⟼ As bases are equal, by equating the powers :

- 5 + 12 = 3m - 2

3m = - 5 + 12 + 2

3m = 9

m = 9/3

$\: \: \: \: \: \: \: \: \boxed{m = 3}$

★ Therefore, the value of m is 3.

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$\begin{gathered}\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}\\\\\end{gathered}$

$\begin{gathered}\qquad \qquad \boxed {\begin{array}{cc} \bf{\underline {\bigstar\:laws \: of \: exponents\::}}\\ \\\\ 1. \: {a}^{m} \times {a}^{n} = {a}^{m + n} \\ \\ 2. \: {a}^{m} \div {a}^{n} = {a}^{m - n} \\ \\ 3. \: ({{a}^{m}})^{n} = {a}^{mn} \\ \\ 4. \: {a}^{0} = 1 \\ \\ 5. \: {a}^{ - m} = \frac{1}{ {a}^{m} } \\ \\ 6. \: \frac{ {a}^{m} }{ {b}^{m} } = ({ \frac{a}{b} })^{m} \\\\ \end{array}} \end{gathered}$

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Hope my Answer is correct and helps you !