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The number $r$ is rational. Which statement about $r^8$ is true?

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Find limits using power and root laws

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Q. The number

r

is rational. Which statement about

r^8

is true?

Determine Product Properties: We need to determine the properties of the product when a rational number $r$ is multiplied by $8$ . A rational number is any number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, with the denominator $q$ not equal to zero. Since $8$ is an integer, and the product of two integers is also an integer, the product $r \times 8$ will be rational because it can be expressed as a fraction where the denominator is not zero.
Multiplication of Rational Number and Integer: To further clarify, the product of any rational number and an integer is always a rational number. This is because multiplying two rational numbers (and an integer is a rational number with a denominator of $1$ ) will result in another rational number. Therefore, $r \times 8$ is rational.
Check for Exceptions: We can also check for any exceptions that might make $r \times 8$ irrational, but since there are no such exceptions (as the multiplication of a rational number by an integer cannot result in an irrational number), we can confidently say that $r \times 8$ is rational.

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