(2^-3*9^3)^-4/2^9*9^-10 which of the following is an equivalent expression to this expression with only positive exponents generated by applying the properties of integer exponents
To simplify the expression, we can apply the properties of integer exponents.
First, let's simplify the numerator:
(2^-3 * 9^3) ^ -4
Using the power of a product property, we can separate the exponents:
(2^-3)^-4 * (9^3)^-4
Now, apply the power of a power property:
2^-12 * 9^-12
Next, let's simplify the denominator:
2^9 * 9^-10
Now, let's combine the expressions:
(2^-12 * 9^-12) / (2^9 * 9^-10)
To simplify this further, we can use the quotient of powers property:
2^-12 / 2^9 * 9^-12 / 9^-10
Now, let's apply the subtracting exponents property:
2^-12-9 * 9^-12-(-10)
Simplifying the exponents:
2^-21 * 9^-2
Finally, we can apply the negative exponent property:
1 / (2^21 * 9^2)
So, the equivalent expression with only positive exponents is:
1 / (2^21 * 9^2)