Brian was asked to write x72 as a product of 2 powers with the same base in 4 different ways, using only positive exponents.

Mathematics

1 answer:

Oksana_A [137]3 years ago

8 0

The equivalent expression to the value given using the laws of indices is ${x}^{4(18)}$

Evaluating the options given based on the laws of indices :

${x}^{8}. {x}^{9} = {x}^{8 + 9} = {x}^{17}$
${x}^{35}. {x}^{47} = {x}^{35 + 47} = {x}^{82}$
${x}^{4(18)} = {x}^{4 \times 18} = {x}^{72}$
${x}^{24}. {x}^{3} = {x}^{24 + 3} = {x}^{27}$

Therefore, the only expression which would give a correct way of representing ${x}^{72} \: is \: {x}^{4(18)}$

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The expression below is scientific notation for what number?<br> 6.1 x 10^6

arlik [135]

Scientific notation is a way to write compactly numbers with lots of digits, either because they're very large (like 2393490000000000000000000), or very small (like 0.0000000000356).

We use powers of ten to describe all those leading/trailing zeros, so that we con concentrate on the significat digits alone.

In your case, the "important" part of the number is composed by the digits 6 and 1, all the other digits are zero. But how many zeroes? Well, let's do the computation.

Every power of 10, $10^n$ is written as one zero followed by n zeroes, so we have

$10^6 = 1000000 \implies 6.1 \times 10^6 =6.1 \times 1000000$

Multiplying a number by $10^n$ means to shift the decimal point to the right and/or add trailing zeroes n times. So, we have to repeat this process six times. We shift the decimal point to the right one position, and then add the five remaning zeroes. The result is thus

$6.1 \times 1000000 = 6100000$