Apply the Properties of Integer Exponents to generate an equivalent expression to (5−3)^6⋅ 5^17/10^−2
answers:
1. 1/20
2. 1/500
3. 20
4. 500
To generate an equivalent expression for (5−3)^6⋅ 5^17/10^−2, we can apply the properties of integer exponents.
First, we can simplify (5−3)^6 to 2^6.
Next, we can simplify 10^−2 to 1/10^2.
Therefore, the equivalent expression is (2^6)⋅(5^17)/(1/10^2).
Using the property (a^m)/(a^n) = a^(m-n), we can simplify the expression further.
(2^6)⋅(5^17)⋅(10^2).
Using the property (a^m)⋅(a^n) = a^(m+n), we can further simplify.
2^6⋅5^17⋅10^2.
Since 2^6 = 64 and 10^2 = 100, the final simplification is:
64⋅(5^17)⋅100.
By multiplying the numbers, we get:
320⋅(5^17).
Therefore, the equivalent expression is 320⋅(5^17).
None of the given answers matches this expression.