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

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: \(1^0 = 1\) \(5^0 = 1\) \( \left( \dfrac{ 23}{89} \right)^0 = 1 \) \( \pi ^ 0 = 1\) \( (-\sqrt{59} )^0 = 1 \)

so zero is one?

i dont get it

Do you know what an exponent is?

number of times the number is multiplied

is the first one 3?

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.)

Yes.

would the second one be 1 then?

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

Yes.

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

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

how would you evaluate 10^-5?

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

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.

|dw:1380743173133:dw|

Join our real-time social learning platform and learn together with your friends!