Question

How do you write $10$ to the $1.5^{th}$ power?

Answer 1

Hint: The student should not get confused with wordings. The student should first distribute $1.5$ as $1.0$& $0.5$. Then the student should use the properties of identities to proceed with the numerical. In this sum student should use the property ${a^x} \times {a^y} = {a^{x + y}}$. Another property of indices which would be useful is ${({a^x})^y} = {a^{xy}}$. It is essential that the student is aware of the property of indices before solving such a sum. If the student is well versed with the chapter on logarithms, he/she can go for that method as well.

Complete Step by Step Solution:
The first step is to convert the given word problem to a simpler form i.e in the form of equation${10^{1.5}}$
Now using the property of indices we can split the given numerical as follows:
${10^{1.5}} = {10^1} \times {10^{0.5}}........(1)$
We can now express the above equation as
${10^{1.5}} = 10 \times \sqrt {10} ........(2)$
Also we need to input the $ \pm $sign as there is a square root.

Thus the answer to the given question is $ \pm 10\sqrt {10} $.

Note: In this particular sum the student should not make the mistake of ignoring the $ \pm $. The answer to a square root should always have this sign as a square of negative numbers can be positive, thus for this reason we will have to include the $ \pm $ sign. Also, any sum which can be solved by indices can be solved by using a logarithm as well. He should assume the base $e$ while solving the sum by the logarithm method. Students should keep in mind that Sums on indices always include the application of multiple properties. Thus they should be thorough with properties while picking up such sums.