To calculate: The simplified form of the expression , 8.0×10122.0×104

Step 1 To simplify this, use the quotient property of radicals, anbn=abn where n is any integer and a,b are any real numbers. 8.0×10122.0×104=8.02.0×1012104 Now, use the exponential property, bmbn=bm−n, where b is any real number and m,n are any integers. 8.0×10122.0×104=8.02.0×1012104 =(2.0)3(2.0)1×1012104 =(2.0)3−1×1012−4 =(2.0)2×108 solving further, 8.0×10122.0×104=(2.0)2×108 =2.0×104 Therefore , hte simplified form of the given expression is (2.0)2×108

Find out the answer to "To calculate: The simplified form of the expression..."

Chesley

Answered question

2021-08-07

To calculate: The simplified form of the expression ,

\sqrt{\frac{8.0 \times 10^{12}}{2.0 \times 10^{4}}}

Answer & Explanation

comentezq

Skilled2021-08-08Added 106 answers

Solution below

2021-12-24

Step 1

To simplify this, use the quotient property of radicals, $\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$

where n is any integer and a,b are any real numbers.

$\sqrt{\frac{8.0 \times 10^{12}}{2.0 \times 10^{4}}} = \sqrt{\frac{8.0}{2.0} \times \frac{10^{12}}{10^{4}}}$

Now, use the exponential property, $\frac{b^{m}}{b^{n}} = b^{m - n}$ , where b is any real number and m,n are any integers.

$\sqrt{\frac{8.0 \times 10^{12}}{2.0 \times 10^{4}}} = \sqrt{\frac{8.0}{2.0}} \times \sqrt{\frac{10^{12}}{10^{4}}}$

$= \sqrt{\frac{(2.0)^{3}}{(2.0)^{1}}} \times \sqrt{\frac{10^{12}}{10^{4}}}$

$= \sqrt{(2.0)^{3 - 1}} \times \sqrt{10^{12 - 4}}$

$= \sqrt{(2.0)^{2}} \times \sqrt{10^{8}}$

solving further, $\sqrt{\frac{8.0 \times 10^{12}}{2.0 \times 10^{4}}} = \sqrt{(2.0)^{2}} \times \sqrt{10^{8}}$

$= 2.0 \times 10^{4}$

Therefore , hte simplified form of the given expression is $\sqrt{(2.0)^{2}} \times \sqrt{10^{8}}$

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