Final answer:
The value of 'a' that makes the equation (5x10³) - (9x10ą) = 4.5x10⁶ true is D) a = 6, since 9 times a power of ten must equal 4,495,000 to balance the equation with both sides having a power of ten of six.
Step-by-step explanation:
The value of 'a' that makes the equation (5x10³) - (9x10ą) = 4.5x10⁶ true is found by algebraically solving for 'a'. First, express the equation with the same power of ten so they can be directly compared:
(5x10³) - (9x10ą) = 4.5x10⁶
(5000) - (9x10ą) = 4500000
To keep the equation balanced, 9x10ą must be equal to 4500000 - 5000, or 4495000. So:
9x10ą = 4495000
10ą = 499444.44...
a = 6 (because 499444.44... is approximately 5x10⁵, which makes 'a' 5 + 1 due to the multiplication by 9)
Therefore, the correct answer is D) a = 6.