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What comes in the place of '*'? ​(216)1.3×(36)1.8÷(6)0.5=6∗(216)^{1.3}×(36)^{1.8}÷(6)^{0.5}=6^*(216)1.3×(36)1.8÷(6)0.5=6∗​​
Question

What comes in the place of '*'?
​(216)1.3×(36)1.8÷(6)0.5=6∗(216)^{1.3}×(36)^{1.8}÷(6)^{0.5}=6^*​​

A.

5

B.

4

C.

7

D.

3

Correct option is C

Given:​
​(216)1.3×(36)1.8÷(6)0.5=6∗(216)^{1.3}×(36)^{1.8}÷(6)^{0.5}=6^∗ 
To find: value of ∗* 
Formula Used: 
​(ax)y=ax×yax×ay=ax+yax÷ay=ax−y(a^x)^y = a^{x \times y} \\ a ^x \times a^y = a^{x+y} \\ a ^x \div a^y = a^{x-y}   
Solution: 
​(216)1.3×(36)1.8÷(6)0.5=6∗(63)1.3×(62)1.8÷(6)0.5=6∗(63.9)×(63.6)÷(6)0.5=6∗63.9+3.6−0.5=6∗67=6∗ Comparing the power as Base is same,∗=7(216)^{1.3}×(36)^{1.8}÷(6)^{0.5}=6^∗ \\ (6^3)^{1.3}×(6^2)^{1.8}÷(6)^{0.5}=6^∗\\(6^{3.9})×(6^{3.6})÷(6)^{0.5}=6^∗ \\ 6^{3.9 + 3.6 - 0.5}=6^∗ \\ 6^7 = 6^* \\ \text{ Comparing the power as Base is same,} \\ * = 7 ​​​​

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