Comparing Very Large and Very Small Numbers

To compare the very large or very small numbers we need to make their exponents same. When their exponents are the same then we can compare the numbers and check which number is large or small.

Example

Compare the two numbers 4.56\times10^8  and 392\times10^7 .

Solution

To compare these numbers we need to make their exponents same.

4.56\times10^8

 392\times10^7=39.2\times10^8

SO

 392\times10^7>4.56\times10^8

1. Find the value of  (4^0+4^{-1})\times2^2

Solution:

(4^0+4^{-1})\times2^2=(1+\frac{1}{4})\times4

 \dfrac{5}{4}\times4

=5

2. Simplify the following expression and express the result in positive power notation:

(-4)^5\div(-4)^8

Solution:

Using \mathrm{a^m\div a^n=a^{m-n}}

(-4)^5\div(-4)^8=\dfrac{(-4)^5}{(-4)^8}

\Rightarrow (-4)^{5-8}=\dfrac{1}{(-4)^3}

3. Evaluate  \mathrm{a^2\times a^3\times a^{-5}}

Solution:

\mathrm{a^2\times a^3\times a^{-5}=a^{2+3-5}}

\mathrm{a^{5-5}}

\mathrm{a^0=1}

4. Evaluate(\sqrt4)^{-3}

Solution:

(\sqrt4)^{-3}=(4^{\frac{1}{2}})^{-3}

 =4^{\frac{-3}{2}}=\dfrac{1}{4^{\frac{3}{2}}}

 =\dfrac{1}{(4^3)^{\frac{1}{2}}}=\dfrac{1}{(64)^{\frac{1}{2}}}

=\dfrac{1}{(8^2)^{\frac{1}{2}}}=\dfrac{1}{8}

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