Question

What is the value of k in the product of powers below? 0 1 -3 -1

Answer 1

The answer is: $k=-1$

The explanation is shown below:

1. By the exponents properties, when you have equal bases, you must sum the exponents of all the bases.

2. Based on this, let's write only the exponents and let's solve for $k$ to calculate its value:

$-3+1+k=-3\\ k=-3+3-1\\ k=-1$

Therefore, the answer is $k=-1$

Answer 2

$10^{-3} \cdot 10 \cdot 10^k = 10^{-3}$

$10^{-3 + 1 + k} = 10^{-3}$

Taking logs,

$-3 + 1 + k = -3$

$k = -1$

Last choice