Answer:
b = 5, c = 13, d = 8.
Step-by-step explanation:
The given expression is [tex]bx^{6} \times cx^{12} \times 9x^{d} = 585x^{26}[/tex]
Now, we have to solve for b, c, and d.
Here, [tex]bx^{6} \times cx^{12} \times 9x^{d} = 585x^{26}[/tex]
⇒ [tex]9bcx^{6 + 12 + d} = 585x^{26}[/tex]
⇒ [tex]9bcx^{18 + d} = 585x^{26}[/tex] ............. (1)
Now, comparing the base terms of both the sides of equation (1) we get,
9bc = 585
⇒ bc = 65 = 5 × 13
Therefore, b = 5 and c = 13 {Since b ≠ 1 and c ≠ 1 and c > b} (Answer)
Now, comparing the power terms of both the sides of equation (1), we get, 18 + d = 26
⇒ d = 8 (Answer)
