To determine whether the equation 10^(−10) = 10 is true or false using the properties of exponents, we need to simplify the expression on both sides and see if they are equal.
First, let's simplify 10^(−10) using the property of negative exponents. The property states that a^(-n) = 1 / a^n.
So, 10^(−10) = 1 / 10^10.
This means that 10^(−10) is a very small number because we are dividing 1 by a large power of 10.
Now, let's simplify 10. We know that any non-zero number raised to the power of 0 is equal to 1. So, 10^0 = 1.
Since 1 / 10^10 is a very small number and 10^0 is equal to 1, the equation 10^(−10) = 10 is clearly false. The justification is that 10^(−10) is not equal to 10 based on the properties of exponents.