6.01 Properties of Exponents
Practice
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Explain why rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is
negative.

Rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is  negative.

Step-by-step explanation:

Considering the expression

Here:

A rational exponent - an exponent that is a fraction -  is the kind of way we may write a root.

If the denominator is an even number, it means we are talking about an even root like square root, 4th root, 6th root etc.

For example, think about squaring a number

-4 × -4 = 16, 4 × 4 = 16

It means any number when it get multiplied by itself an even number of times, it would always yield a positive number.

It is not possible to take the square root of a negative number as we can not yield a negative number when we square the number. In other words, there is no way we can multiply the same negative number twice and get a negative number. This is why is undefined.

Therefore, rational exponents are not defined when the denominator of the exponent in lowest terms is even and the base is  negative.

5104.38 inches

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .