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Find the value of  a×a3/2×a2×a5/2×a3×a7/2×a4×a9/2×a5a \times a^{3/2} \times a^2 \times a^{5/2} \times a^3 \times a^{7/2} \times a^4 \times a
Question

Find the value of  a×a3/2×a2×a5/2×a3×a7/2×a4×a9/2×a5a \times a^{3/2} \times a^2 \times a^{5/2} \times a^3 \times a^{7/2} \times a^4 \times a^{9/2} \times a^5

A.

a²²

B.

a²⁷

C.

a²⁹

D.

a³¹

Correct option is B

Given:
a×a3/2×a2×a5/2×a3×a7/2×a4×a9/2×a5a \times a^{3/2} \times a^2 \times a^{5/2} \times a^3 \times a^{7/2} \times a^4 \times a^{9/2} \times a^5 ​​

Formula:
When multiplying powers with the same base, add the exponents:

am × an = a​(m + n)

Solution:
Add the exponents:
= 1 + 3/2 + 2 + 5/2 + 3 + 7/2 + 4 + 9/2 + 5
= (1 + 2 + 3 + 4 + 5) + (3/2 + 5/2 + 7/2 + 9/2)
= 15 + (3 + 5 + 7 + 9)/2
= 15 + 24/2
= 15 + 12
= 27

Final Answer:

(b) a27

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