Select all the expressions that are equivalent to ( g^8 )^2.
1. 1 / 9^10
2. 9^16
3. 1 / 9^-16
4. 1 / 9^16
Select all the expressions that are equivalent to ( g^8 )^2
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Select all the expressions that are equivalent to ( g^8 )^2.
1. 1 / 9^10
2. 9^16
3. 1 / 9^-16
4. 1 / 9^16
To simplify ((g^8)^2), you use the power of a power rule which states that ((a^m)^n = a^{mn}).
So, ((g^8)^2 = g^{8 times 2} = g^{16}).
Now, to express this in terms of base 9, we can note that if (g = 9), then (g^{16} = 9^{16}).
Let’s express the given options with respect to this:
1. (1 / 9^{10}) is not equivalent.
2. (9^{16}) is equivalent to (g^{16}).
3. (1 / 9^{-16} = 9^{16}) (since dividing by a negative exponent is the same as multiplying by the positive exponent, so this is also equivalent).
4. (1 / 9^{16}) is not equivalent.
Thus, the correct answers are: 2 and 3.
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