If 5 y – 5 ( y − 1 ) = 100 , then what is the value of ( 3 y ) y ? Options: A . &nbsp256 B . &nbsp343 C . &nbsp216 D . &nbsp729

Answer: Option D : D 5 y − 5 y 5 = 100 ; 5 y ( 1 − 1 5 ) = 5 2 × 4 ; 5 y ( 4 5 ) = 5 2 × 4 ⟹ 5 ( y − 1 ) × 4 = 5 2 × 4 ; y − 1 = 2 ; y = 3. Answer is ( 3 y ) y = ( 9 ) 3 = 729 .

If 5y–5(y−1)=100, then what is the value of (3y)y?

Question

5^{y} - 5^{(y - 1)} = 100

, then what is the value of

(3 y)^{y}

Options:

A . 256

B . 343

C . 216

D . 729

Answer: Option D
:
D

5^{y} - \frac{5^{y}}{5} = 100; 5^{y} (1 - \frac{1}{5}) = 5^{2} \times 4; 5^{y} (\frac{4}{5}) = 5^{2} \times 4

⟹ 5^{(y - 1)} \times 4 = 5^{2} \times 4; y - 1 = 2; y = 3.

Answer is

(3 y)^{y} = (9)^{3} = 729

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