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Why do whole numbers raised to an exponent get greater and greater while fractions raised to an exponent get smaller?
Whole numbers raised to an exponent increase because multiplying a whole number by itself repeatedly results in a larger product. Conversely, fractions (a number less than one) raised to an exponent get smaller because each multiplication reduces the value further; for example, multiplying 0.5 by itself yields 0.25, which is less than 0.5. Thus, the behavior of whole numbers and fractions under exponentiation is fundamentally different due to their values relative to one.
Why do whole numbers raised to an exponent get greaterwhile fractions raised to an exponent get smaller?
Whole numbers greater than one raised to an exponent increase because multiplying a number by itself repeatedly results in a larger value. In contrast, fractions (numbers between 0 and 1) raised to an exponent decrease because each multiplication reduces the value further, as each factor is less than one. Thus, while whole numbers amplify their size, fractions diminish with each exponentiation.
What is a base in the laws of exponents?
If you have a power, the "base" is the large number to the left; the "exponent" is the raised (and smaller) number to the right.
What is the number that is raised to a power called?
an exponent
When multiplying fractions with variables if there is no exponent do you add one?
Yes.
Why do whole numbers raised to an exponent get greater and greater while fractions raised to an exponent get smaller?
Whole numbers raised to an exponent increase because multiplying a whole number by itself repeatedly results in a larger product. Conversely, fractions (a number less than one) raised to an exponent get smaller because each multiplication reduces the value further; for example, multiplying 0.5 by itself yields 0.25, which is less than 0.5. Thus, the behavior of whole numbers and fractions under exponentiation is fundamentally different due to their values relative to one.
Why do whole numbers raised to an exponent get greaterwhile fractions raised to an exponent get smaller?
Whole numbers greater than one raised to an exponent increase because multiplying a number by itself repeatedly results in a larger value. In contrast, fractions (numbers between 0 and 1) raised to an exponent decrease because each multiplication reduces the value further, as each factor is less than one. Thus, while whole numbers amplify their size, fractions diminish with each exponentiation.
Can you have more than one exponent on top of a number?
Yes, you can, but it starts getting complicated. You can, for example have a number raised to an exponent that is itself a number raised to an exponent, or you can have a number raised to an exponent and the result raised to another exponent.
What is a base in the laws of exponents?
If you have a power, the "base" is the large number to the left; the "exponent" is the raised (and smaller) number to the right.
What is the smallest raised number in a power that tells how many times the base is used as a factor?
The exponent.
Why do whole numbers raised to exponents get greater while fractions raised to exponent get smaller?
An exponent just tells how many times a number is multiplied by itself. With whole numbers, if you keep multiplying them, they have to increase. 3 x 3 is 9, 3 x 3 x 3 is 27 and so on. Taking a half of anything makes it smaller. 1/2 x 1/2 is 1/4, 1/2 x 1/2 x 1/2 is 1/8 and so on.
What does 2 with an exponent of 3 equal in fractions?
8
What is the number that is raised to a power called?
an exponent
What is the number that is raised to and exponent?
its called a base :)
When multiplying fractions with variables if there is no exponent do you add one?
Yes.
How do we use negative exponent in real life?
In calculating fractions.
When a number is raised to a power what is it called?
The power could then be called an exponent. The number that is being raised to a power is called the base. In the case of 42, the exponent is 2 and the base is 4.
