Question

the radius of neptune is about $2.4 \cdot 10^4$ km. the radius of venus is about $6 \cdot 10^3$ km. how many times greater is the radius of neptune than the radius of venus? well rewrite the numerator with the same power of 10 as the denominator. fill in the missing factor to write an equivalent expression to $2.4 \cdot 10^4$. $\dfrac{\text{radius of neptune}}{\text{radius of venus}} = \dfrac{2.4 \cdot 10^4}{6 \cdot 10^3} = \dfrac{? \cdot 10^3}{6 \cdot 10^3}$ $2.4 \cdot 10^4$ $2.4 \cdot 10^{\square} \cdot 10^3$

Explanation:

Step1: Recall exponent rule

We know that \(10^{a + b}=10^a\times10^b\). For \(10^4\), we can write it as \(10^{1 + 3}=10^1\times10^3\).

Step2: Substitute and simplify

Given \(2.4\times10^4\), substitute \(10^4 = 10\times10^3\), so \(2.4\times10^4=2.4\times10\times10^3\). Calculate \(2.4\times10 = 24\). So \(2.4\times10^4 = 24\times10^3\).

Answer:

The missing factor is \(24\) and the missing exponent (in the box) is \(1\). For the first missing factor (the "?"): \(24\); for the box: \(1\)