what is the value of n in this equation? enter your answer in the box. (2.4×10³)×(3×10ⁿ)=7.2×10⁹

Explanation:

Step1: Multiply the coefficients

First, multiply the non - exponential parts: $2.4\times3 = 7.2$.

Step2: Use the rule of exponents for multiplication

According to the rule $a^m\times a^n=a^{m + n}$, we have $(10^{3})\times(10^{n})=10^{3 + n}$. So the left - hand side of the equation becomes $7.2\times10^{3 + n}$.

Step3: Set up the equation for the exponents

Since $7.2\times10^{3 + n}=7.2\times10^{9}$, then $3 + n=9$.

Step4: Solve for n

Subtract 3 from both sides of the equation $3 + n=9$: $n=9 - 3$. $n = 6$

Answer:

$6$