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Mathematics
OpenStudy (anonymous):

Evaluate the expressions 3(4/5)^0 (-2)^0

OpenStudy (mathstudent55):

Zero exponent is defined like this: \(a^0 = 1\) for all \(a\) except \(a = 0\). In other words any number, other than zero, raised to the zero power is equal to 1. Examples: \(1^0 = 1\) \(5^0 = 1\) \( \left( \dfrac{ 23}{89} \right)^0 = 1 \) \( \pi ^ 0 = 1\) \( (-\sqrt{59} )^0 = 1 \)

OpenStudy (anonymous):

so zero is one?

OpenStudy (anonymous):

i dont get it

OpenStudy (mathstudent55):

Do you know what an exponent is?

OpenStudy (anonymous):

number of times the number is multiplied

OpenStudy (anonymous):

is the first one 3?

OpenStudy (mathstudent55):

Right, that is true if the exponent whole number, 2 or greater. An exponent of 2 means multiply the number by itself. \(5^2 = 5 \times 5 = 25\) (We used two fives because of the exponent 2.)

OpenStudy (mathstudent55):

Yes.

OpenStudy (anonymous):

would the second one be 1 then?

OpenStudy (mathstudent55):

For exponent one, there is a special definition. \(a^1 = a\) A number raised to exponent 1 is equal to itself. \(5^1 = 5\) \((-6)^1 = -6 \)

OpenStudy (mathstudent55):

Yes.

OpenStudy (mathstudent55):

Exponent zero also has a special definition, which is already explained above.

OpenStudy (mathstudent55):

\(3 \left(\dfrac{4}{5} \right)^0 = 3 \times 1 = 3\) \( (-2)^0 = 1\)

OpenStudy (anonymous):

how would you evaluate 10^-5?

OpenStudy (mathstudent55):

Negative exponent has its own definition. Here it is: For any \(a\), \(a \ne 0\) \(a^{-n} = \dfrac{1}{a^n} \)

OpenStudy (mathstudent55):

To turn a negative exponent into a positive exponent, write the expression with a positive exponent and place it in the denominator of a fractiom with numerator 1.

OpenStudy (mathstudent55):

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