Question

Simplify and write in exponential form (3^6 ÷ 3^8 ) ^4 × 3^-4

Answer 1

SOLUTION

TO DETERMINE

$\sf{ {( \: {3}^{6} \: \div \: {3}^{8} \: )}^{4} \times {3}^{ - 4} }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\sf{1. \: \: {a}^{m} \: \div \: {a}^{n} \: = {a}^{m - n} }$

$\sf{2. \: {( {a}^{m}) }^{n} = {a}^{mn} }$

EVALUATION

$\sf{ {( \: {3}^{6} \: \div \: {3}^{8} \: )}^{4} \times {3}^{ - 4} }$

$\sf{ = {( \: {3}^{6 - 8} )}^{4} \times {3}^{ - 4} }$

$\sf{ = {( \: {3}^{ - 2} )}^{4} \times {3}^{ - 4} }$

$\sf{ = {3}^{ - 8} \times {3}^{ - 4} }$

$\sf{ = {3}^{ (- 8 - 4)} }$

$\sf{ = {3}^{ - 12} }$

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Answer 2

Answer:

(3^6 ÷ 3^8) ^4 x 3^-4

= (3^6-8) ^4 x 3^-4

= (3^-2) ^4 x 3^-4

= 3^-8 x 3^-4

= 3^-8-4

=3^-12

=1/3^12

Step-by-step explanation: