Question

what is the value of x in the product of powers below?

(6^{9} \cdot 6^{x} = 6^{2})

-11
-7
7
11

Explanation:

Apply the product rule of exponents

$$ 6^9 \cdot 6^x = 6^{9 + x} $$

Set up the equation for the exponents

$$ 9 + x = 2 $$

Solve for x

$$ x = 2 - 9 = -7 $$

Answer:

• -11
• -7 (Correct answer)
• 7
• 11