Question

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

Answer 1

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:

\(1^0 = 1\)

\(5^0 = 1\)

\( \left( \dfrac{ 23}{89} \right)^0 = 1 \)

\( \pi ^ 0 = 1\)

\( (-\sqrt{59} )^0 = 1 \)

Answer 2

so zero is one?

Answer 3

i dont get it

Answer 4

Do you know what an exponent is?

Answer 5

number of times the number is multiplied

Answer 6

is the first one 3?

Answer 7

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.)

Answer 8

Yes.

Answer 9

would the second one be 1 then?

Answer 10

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

Answer 11

Yes.

Answer 12

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

Answer 13

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

\( (-2)^0 = 1\)

Answer 14

how would you evaluate 10^-5?

Answer 15

Negative exponent has its own definition.

Here it is:

For any \(a\), \(a \ne 0\)

\(a^{-n} = \dfrac{1}{a^n} \)

Answer 16

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.