### Video Transcript

Find the value of 4.1 multiplied by 10 to the power of three multiplied by nine multiplied by 10 to the power of seven giving your answer in scientific notation.

Our first step is to multiply 4.1 by nine. This gives us 36.9. Using one of the laws of indices — 𝑥 to the power of 𝑎 multiplied by 𝑥 to the power of 𝑏 equals 𝑥 to the power of 𝑎 plus 𝑏 — enables us to multiply 10 cubed by 10 to the power of seven as we are able to add the exponents — in this case three and seven — to give us 10 to the power of 10.

In order to write an answer in scientific notation, the first part must be between one and 10. Currently, 36.9 is too large. We can rewrite 36.9 as 3.69 multiplied by 10. Using our laws of indices once again, we get a final answer of 3.69 times 10 to the power of 11.

This means that the value of 4.1 multiplied by 10 cubed multiplied by nine multiplied by 10 to the power of seven is equal to 3.69 times 10 to the power of 11.