Question

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

6^9 x 6^x =6^2
A)-11
B) -7
C)7
D)11

Answer 1

To find the value of x in the expression 6^9 \( \times \) 6^x = 6^2, we add the exponents (since the bases are the same) and solve for x, resulting in x = -7.

Step-by-step explanation:

The value of x in the product of powers 6^9 \( \times \) 6^x = 6^2 can be determined using the laws of exponents. Specifically, when we multiply expressions with the same base, we add their exponents. Thus, the equation becomes 6^(9+x) = 6^2. To solve for x, we equate the exponents because the bases are already equal: 9 + x = 2. Solving for x, we get x = 2 - 9 which simplifies to x = -7. Therefore, the correct answer is option B) -7.

Answer 2

To find the x in the equation 6^9 * 6^x = 6^2, we can add the exponents because the bases are the same. By adding 9 and x, we get 2. Solving for x, we find that x is -7.

Step-by-step explanation:

To find the value of x in the given equation, we need to use the property of exponents that states when two numbers with the same base are multiplied together, the exponents can be added. Applying this property to the equation, we have 6^9 * 6^x = 6^2.

Since the bases are the same, we can add the exponents: 9 + x = 2.

Now we can solve for x by subtracting 9 from both sides: x = 2 - 9 = -7.

Therefore, the value of x is -7.