Question

evaluate the expression. \\((3.2 \times 10^4) \times (1.5 \times 10^3)\\) \\(\boxed{?} \times 10^{\boxed{?}}\\)

Explanation:

Step1: Multiply the coefficients

Multiply 3.2 and 1.5.
$3.2\times1.5 = 4.8$

Step2: Add the exponents of 10

For numbers in scientific notation $a\times10^m$ and $b\times10^n$, when multiplying, we add the exponents: $10^m\times10^n = 10^{m + n}$. Here, $m = 4$ and $n = 3$, so $10^4\times10^3 = 10^{4 + 3}=10^7$

Step3: Combine the results

Combine the coefficient from Step1 and the power of 10 from Step2. So the expression becomes $4.8\times10^7$

Answer:

$4.8\times 10^{7}$ (So the first box is 4.8 and the second box is 7)