(01.03 LC)
What is the value of 4 to the power of 6 over 4 to the power of 8? (1 point)
4^6/4^8
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4^6/4^8 = 4^6/(4^6*4^2)= 1/4^2 = 1/16
To find the value of 4 to the power of 6 over 4 to the power of 8, we can simplify the expression using the properties of exponents.
The property that states "When dividing two exponential expressions with the same base, subtract the exponents" can be used in this case.
So, we subtract the exponent of the denominator from the exponent of the numerator:
4^6 ÷ 4^8 = 4^(6-8) = 4^(-2)
Notice that when the exponent is negative, it means we are working with a fraction. To evaluate this expression further, we can rewrite it as:
4^(-2) = 1 / 4^2
So, the value of 4 to the power of 6 over 4 to the power of 8 is equal to 1/4^2.
Simplifying 1/4^2, we can calculate:
1 / 4^2 = 1 / 16
Therefore, the value of 4 to the power of 6 over 4 to the power of 8 is 1/16.