(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

Answer 1

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)