Question

(3^8÷3^-6)×(9^-2)^3​

Answer 1

Answer:

(3^14 )x (3^-4)^3

=3^14 x 3^-12

=3^14-12

=3^2

=9

There fore answer = 9

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Answer 2

Answer:

$( {3}^{8} \div {3}^{ - 6} ) \times {( {9}^{ - 2} )}^{3}$

Take numbers with negative index to the denominator

$( {3}^{8} \div \frac{1}{ {3}^{6} } ) \times {( \frac{1}{ {9}^{2} } )}^{3}$

Change division sign to multiplication sign

$( {3}^{8} \times {3}^{6} ) \times{( \frac{1}{ {9}^{2} } )}^{3}$

If two numbers having same magnitude are multiplied, their indices is added. Add indices of 3.

$( {3}^{8 + 6} ) \times{( \frac{1}{ {9}^{2} } )}^{3}$

$( {3}^{14} ) \times{( \frac{1}{ {9}^{2} } )}^{3}$

Index outside the bracket is multiplied to each index inside the bracket. 1 raised to any power is still 1. So let's not show 1^3.

$( {3}^{14} ) \times( \frac{1}{ {9}^{2 \times 3} })$

$( {3}^{14} ) \times( \frac{1}{ {9}^{6} })$

9 can be written as 3 squared

$( {3}^{14} ) \times( \frac{1}{ { ({3}^{2} })^{6} })$

Again take index inside the bracket. This time I will directly multiply

$( {3}^{14} ) \times( \frac{1}{ {3}^{12} })$

Multiply the fraction

$\frac{ {3}^{14} }{ {3}^{12} }$

If two numbers having same magnitude are divided, their indices is subtracted. Subtract indices of 3.

${3}^{14 - 12}$

${3}^{2}$

$9$

Step-by-step explanation:

Proof:

$( {3}^{8} \div {3}^{ - 6} ) \times { ( {9}^{ - 2} ) }^{3}$

$(6561 \div \frac{1}{729} ) \times {( \frac{1}{81}) }^{3}$

$(6561 \times 729) \times ( \frac{1}{ {81}^{3} } )$

$(4782969) \times ( \frac{1}{531441})$

$\frac{4782969}{531441}$

$9$