Question

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

Answer 1

Answer:

= -7

Step-by-step 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

Answer 2

Answer:

x=-7

Step-by-step 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

$x=-7$