Question

Evaluate 3^4 × 12^3 × 36 / 2^5 × 6^3

Answer 1

step by step explained

Step-by-step explanation:

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Answer 2

The correct answer to the given expression is 729.

Given,

The expression = $\frac{3^{4}*12^{3} *36 }{2^{5}*6^{3} }$.

To Find,

The value of the given expression,

Solution,

Let's solve the given expression,

=  $\frac{3^{4}*12^{3} *36 }{2^{5}*6^{3} }$.

On Simplifying the powers, we get

=  $\frac{3^{4}*(2^{2} *3)^{3} *6^{2} }{2^{5}*(2*3)^{3} }$.

On Solving the brackets,

=  $\frac{3^{4}*2^{2*3} *3^{3} *(2*3)^{2} }{2^{5}*2^{3} *3^{3} }$.

=  $\frac{3^{4}*2^{2*3} *3^{3} *2^{2} *3)^{2} }{2^{5}*2^{3} *3^{3} }$.

Arranging the same bases together,

=  $\frac{3^{4}*3^{3} *3^{3} *2^{6} *2^{2} }{2^{5}*2^{3} *3^{3} }$.

Now we will add the powers of the same bases,

= $\frac{3^{4+3+2}*2^{6+2} }{2^{5+3}*3^{3} }$

On adding the powers, we get,

= $\frac{3^{9}*2^{8} }{2^{8}*3^{3} }$

We will eliminate the numbers with the same power,

= 3⁹ ÷ 3³

In divide, the powers get subtracted,

So, we get,

= 3⁶

= 3 × 3 × 3 × 3 × 3 × 3

On multiplying, we get,

= 729.

The correct answer to the given expression is 729.

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