Question

ᴇᴠᴀʟᴜᴀᴛᴇ ᴛʜɪꜱ ᴩʟᴇᴀꜱᴇ ꜰᴀꜱᴛ​

Answer 1

Question :

$\bf{\gray{ {2}^{3} \times ( {6}^{ - 4} \: \div {6}^{ - 2} )}}$

Answer :

$= \bf{\pmb{\green{ {2}^{3} \times ( \frac{1}{ {6}^{4} } \: \div \frac{1}{ {6}^{2} } )}}}$

$= \bf{\pmb{\green{ 8 \: \times ( \frac{1}{ {1296} } \: \div \frac{1}{ 36} )}}}$

$= \bf{\pmb{\green{ 8 \: \times ( \frac{1296}{ {1} } \: \times \frac{1}{ 36} )}}}$

$= \bf{\pmb{\green{ 8 \: \times ( \frac{\cancel{1296} \:{\pink{36}}}{{1} } \: \times \frac{1}{\cancel{ 36} \: \pink{1}} )}}}$

$= \bf{\pmb{\green{8 \: \times 36}}}$

$= \boxed{\bf{\pmb{\green{288}}}}$

$\therefore \tt{\: answer \: = \: 288}$

Answer 2

Given Question :

Evaluate $\tt \: 2^3 \: \times (6^ {- 4} \: \div \: 6^ {- 2} )$

Solution :

Here, first let's change the negative exponent to positive. in order to express $\bf a^{-m}$ it goes into reciprocal.

$\implies \tt \: {2}^{3} \times \dfrac{1}{ {6}^{4} } \div \dfrac{1}{{6}^{2} } \\ \\ \implies \tt \: 8 \times \dfrac{1}{1296} \div \dfrac{1}{36}$

Now we need to transpose the numerators and denominators in second expression in order to perform multiplication,

$\implies \tt \: 8 \times \bigg( \dfrac{1296}{1} \times \dfrac{1}{36} \bigg) \\ \\ \implies \tt \: 8 \times \dfrac{36}{\cancel{1} } \\ \\ \implies \large\underline{ \boxed{ \tt{ \green{288}}}} \sf{ \pink{_{(Required \: Answer)}}}$

$\therefore \underline{ \sf{The \: answer \: is \: \bf 288}}$

Additional Information :

$\red{\dag}$ Laws of exponents :

1. $\large\bf a^{m} \times a^{n}$

• $\sf a^{m + n}$

2. $\large\bf a^{m} ÷ a^{n}$

• $\sf a^{m - n}$

3. $\large\bf a^{m} \times b^{m}$

• $\sf (a \times b)^{m}$

4. $\large\bf a^{m} ÷ b^{m}$

• $\sf (a ÷ b)^{m}$ or $\sf \dfrac{a ^{m}}{b ^{m}}$

5. The value of a⁰ :-

• $\boxed{\tt{a^{0} = 1}}$