81^3/4 / 81^1/2
A. 9
B. 27
C. (81/3)^-1/2
D. 3

Step-by-step explanation:

81^(0.75) / 81^(0.5)

= 81^(0.25)

= 3. (because 3⁴ = 81)

Step-by-step explanation:

[(81)^3/4/(81)^1/2]

Solve and choose the correct option.

A. 9

B. 27

C. (81/3)^-1/2

D. 3

[(81)^3/4/(81)^1/2]

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1/2 from 3/4 to get 1/4.

=> (81)^3/4 - 1/2

Take the LCM of 4 and 2 in power 81 in denominator and get 4.

=> (81)^3-2/4

=> (81)^1/4

Now, 81 can written as 3⁴ in using exponent rule.

=> (3^4)^1/4

=> 3^4×1/4

In power of 2 both 4 will cancel out in one time.

=> 3^1

=> 3 Ans.

Hope this helps.

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step-by-step explanation: