Question

Please answer this math question

Answer 1

Here we have the sum related to exponents and powers which is to solved by using the laws of exponents !! Here , we have to find the value of ' x '

$\large \tt{{ \frac{2}{3} }^{12} = { \frac{3}{2} }^{ - 3x} } \\ \implies \large \tt{{ \frac{2}{3} }^{12} = { \frac{2}{3} }^{ 3x}} \\ { \boxed {\tt{Since \: powers \: are \: equal \: bases \: can \: be \: equated !! }}} \\ \large \implies \tt{12 = 3x}\\ \large \implies \tt{ \frac{12}{3} = x}\\ \large \implies \tt{ x = 4}$

Here ,

Laws of exponents used :

$\purple{ \tt{ {x}^{ - 1} = \frac{1}{ {x}^{1}}}}$

Additional Information :

• Exponents are also called Powers or Indices.
• To write the large numbers in short form, we use exponents.
• The exponent of a number tells how many times to use the number in a multiplication.
• Any number with zero exponents is equal to one irrespective of the base.
• If we have to multiply the powers which have the same base then we have to add the exponents.

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$