Math, asked by romisharmastudent15, 5 hours ago

ᴇᴠᴀʟᴜᴀᴛᴇ ᴛʜɪꜱ ᴩʟᴇᴀꜱᴇ ꜰᴀꜱᴛ​

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Answers

Answered by Anushka786
12

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}

Answered by Clαrissα
15

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}}
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