### Video Transcript

Find the value of 4.4 multiplied by 10 to the power of negative two divided by 1.1 times 10 to the power of negative six, giving your answer in standard form.

Rewriting this calculation, we can see that we can split the two parts, 4.4 divided by 1.1 and 10 to the power of negative two divided by 10 to the power of negative six. Dividing 4.4 by 1.1 gives us four. In order to simplify 10 to the power of negative two divided by 10 to the power of negative six, we need to use one of the laws of exponents. 𝑥 to the power of 𝑎 divided by 𝑥 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 minus b. This law only works if the base number, in our example 10, is exactly the same. Subtracting the exponents or powers gives us negative two minus negative six. This gives us positive four or four, which means that 10 to the power of negative two divided by 10 to the power of negative six is 10 to the power of four. Therefore, the value of 4.4 times 10 to the power of negative two divided by 1.1 multiplied by 10 to the power of negative six is four multiplied by 10 to the power of four.

As we know that 10 to the power of four is 10 multiplied by 10 multiplied by 10 multiplied by another 10 which equals 10000, we could also have written our answer as four multiplied by 10000 which gives us 40000. Therefore, our answer: four multiplied by 10 to the power of four can also be written as 40000.

An alternative or a bit more long-winded method would be to rewrite 4.4 multiplied by 10 to the power of negative two as 0.044 and to rewrite 1.1 multiplied by 10 to the power of negative six as 0.0000011. The exponents in this case, negative two and negative six, tell us how many times we need to move the decimal point, or how many times the numbers move along in place value. Multiplying the top and the bottom of this equation by 1000000 gives us 440000 divided by 11. As 44 divided by 11 is four, we’re left with an answer of 40000.

This can then be rewritten in standard form as four multiplied by 10 to the power of four, which is exactly the same answer as we got with our first method.