Question

calculate.
$(8 \times 10^4)(9 \times 10^2)$
write your answer in scientific notation.

Explanation:

Step1: Multiply the coefficients

Multiply 8 and 9: $8\times9 = 72$

Step2: Add the exponents of 10

For $10^4$ and $10^2$, use the rule $a^m\times a^n=a^{m + n}$. So $10^4\times10^2=10^{4 + 2}=10^6$

Step3: Combine the results and adjust to scientific notation

We have $72\times10^6$. But scientific notation requires the coefficient to be between 1 and 10. So rewrite 72 as $7.2\times10^1$. Then $72\times10^6=7.2\times10^1\times10^6$. Using the exponent rule again, $10^1\times10^6 = 10^{1+6}=10^7$. So the result is $7.2\times10^7$

Answer:

The coefficient is $7.2$ and the exponent of 10 is $7$, so the answer is $7.2\times10^{7}$ (filling the first box with $7.2$ and the second box with $7$)