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Do a negative integer raised to an even power always results in a positive integer?
Yes.
Why does a negative integer raised to an even power always result in a negative integer?
A negative integer raised to an even power results in a positive integer, not a negative integer. This occurs because multiplying a negative number by itself an even number of times cancels out the negative signs. For example, ((-2)^2 = 4) and ((-3)^4 = 81), both of which are positive. Therefore, the statement is incorrect; a negative integer raised to an even power is always positive.
How is a negative integer power on a base related to the corresponding positive integer power on that base?
A negative integer power of a base is the reciprocal of the base raised to the corresponding positive integer power. For example, ( a^{-n} = \frac{1}{a^n} ), where ( a ) is the base and ( n ) is a positive integer. This relationship shows that as the exponent decreases into the negatives, the value of the expression represents a division by the base raised to the positive power.
Is a to the 3rd power greater than or equal to a for all integer values of A and why?
No. A negative integer raised to the third power will yield a negative number that is less than the integer. Only whole numbers (positive integers greater than or equal to 1) have the property where that integer raised to the third power is greater than or equal to the integer.
How can you. Evaluate a nonzero number with a negative integer exponent?
To evaluate a nonzero number with a negative integer exponent, you can use the rule that states ( a^{-n} = \frac{1}{a^n} ), where ( a ) is the nonzero number and ( n ) is the positive integer. For example, ( 2^{-3} ) can be evaluated as ( \frac{1}{2^3} = \frac{1}{8} ). This method effectively converts the negative exponent into a positive one by taking the reciprocal of the base raised to the corresponding positive exponent.
Do a negative integer raised to an even power always results in a positive integer?
Yes.
Why does a negative integer raised to an even power always result in a negative integer?
A negative integer raised to an even power results in a positive integer, not a negative integer. This occurs because multiplying a negative number by itself an even number of times cancels out the negative signs. For example, ((-2)^2 = 4) and ((-3)^4 = 81), both of which are positive. Therefore, the statement is incorrect; a negative integer raised to an even power is always positive.
Why does a negative integer raised to an even power always result in a positive integer?
The multiplication rule of thumb always states that a negative number times a negative number results in a positive number. Since an even number is always divisible by two, any value raised to an even integer power will result in a positive number. However, a basic proof is presented as follows: (-A) * (-A) = A^2 ((-A) * (-A)) ^ 2 = ((-A * -A) * (-A * -A)) = A^2 * A^2 = A ^ 4 ...
How is a negative integer power on a base related to the corresponding positive integer power on that base?
A negative integer power of a base is the reciprocal of the base raised to the corresponding positive integer power. For example, ( a^{-n} = \frac{1}{a^n} ), where ( a ) is the base and ( n ) is a positive integer. This relationship shows that as the exponent decreases into the negatives, the value of the expression represents a division by the base raised to the positive power.
Is a to the 3rd power greater than or equal to a for all integer values of A and why?
No. A negative integer raised to the third power will yield a negative number that is less than the integer. Only whole numbers (positive integers greater than or equal to 1) have the property where that integer raised to the third power is greater than or equal to the integer.
Why is any number raised to a even power positive?
A positive number times a positive number is always positive. A negative number times a negative number is always positive. Therefore, any square number will be positive. Any number to the fourth power (a square times a square) will always be positive. And so on.
A negative number raised to an even power will be positive or negative?
Positive
How can you. Evaluate a nonzero number with a negative integer exponent?
To evaluate a nonzero number with a negative integer exponent, you can use the rule that states ( a^{-n} = \frac{1}{a^n} ), where ( a ) is the nonzero number and ( n ) is the positive integer. For example, ( 2^{-3} ) can be evaluated as ( \frac{1}{2^3} = \frac{1}{8} ). This method effectively converts the negative exponent into a positive one by taking the reciprocal of the base raised to the corresponding positive exponent.
Can you show me examples that a negative integer raised to an even power always results in an positive integer?
-32 this is like saying (-3)(-3) and a double negative is positive -34 this is like saying (-3)(-3)(-3)(-3) since there is two double negatives it is still positive -36 this is like saying (-3)(-3)(-3)(-3)(-3)(-3) since there is three double negatives it is still positive -38 this is like saying (-3)(-3)(-3)(-3)(-3)(-3)(-3)(-3) since there is four double negatives it is still positive This can apply for any negative integer.
Can an exponent be a negative number?
Yes, an exponent can be a negative number. When a base is raised to a negative exponent, it is equivalent to taking the reciprocal of the base raised to the positive exponent. For example, ( a^{-n} = \frac{1}{a^n} ) where ( a ) is a non-zero number and ( n ) is a positive integer. This concept is commonly used in mathematics to simplify expressions and solve equations.
What is positive times power that is negative?
When a positive number is raised to a negative power, it results in a positive fraction. Specifically, if ( a ) is a positive number and ( n ) is a positive integer, then ( a^{-n} = \frac{1}{a^n} ). This means that the value decreases as the exponent becomes more negative, but the result remains positive. For example, ( 2^{-3} = \frac{1}{2^3} = \frac{1}{8} ).
When is a negative number raised to an odd power negative?
It is always negative when raised to an odd power and always positive when raised to an even power -2 to the third power = -2 x -2 x -2 = -8 -2 to the fourth power = -2 x -2 x -2 x -2 = +16
