Question

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

Answer 1

x=-7

Explanation:

`6^9 \cdot 6^x = 6^2`

Apply exponential property to solve for x

`a^m \cdot a^n = a^(m+n)`

`6^9 \cdot 6^x = 6^(9+x)`

So the given equation becomes

`6^(9+x)= 6^2`

Both sides of the equation has same base 6

So we equate the exponent and solve for x

`9+x= 2`

Subtract 9 from both sides

`x=-7`

Answer 2

= -7

Explanation:

6 ⁹ ×6^x = 6²

From the laws of indices;

aⁿ × aⁿ = a^2n

Therefore;

6 ⁹ ×6^x = 6^(9+x)

6^(9+x) = 6²,

Since the bases are the same then the exponents are equal;

9+x = 2

x = -7