Evaluate 6.28 square root of 100^-12*1^-3

Problem

6.28√(,100(−12)⋅1(−3))

Solution

1. Simplify the term 1(−3) by noting that any power of 1 is equal to 1

1(−3)=1

2. Substitute the simplified value back into the expression.

6.28√(,100(−12)⋅1)

6.28√(,100(−12))

3. Apply the property of square roots √(,xn)=x(n/2) to the term 100(−12)

√(,100(−12))=100(−12/2)

100(−6)

4. Rewrite the expression using the result of the square root.

6.28⋅100(−6)

5. Convert the expression into standard scientific notation.

6.28×10(−12)

Final Answer

6.28√(,100(−12)⋅1(−3))=6.28×10(−12)

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