Question

Apply the property of negative integer exponents to generate an expression equivalent to 5 to the power of -9 over 4 to the power of -12 with positive exponents only

Answer 1

To apply the property of negative integer exponents, we can rewrite the expression as:

(1 / 5^9) / (1 / 4^12)

Next, we can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

(1 / 5^9) * (4^12 / 1)

Now, let's simplify each term:

1 / 5^9 = 1 / (1 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5) = 1 / 1953125

4^12 = 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 * 4 = 16777216

Now, let's substitute these simplified terms back into the expression:

(1 / 1953125) * (16777216 / 1)

Finally, we can multiply these two terms together to get the final expression:

1 / (1953125 * (1 / 16777216))

Simplifying further, we get:

1 / (1953125 / 16777216)

To simplify this division, we can multiply the numerator and denominator by the reciprocal of the denominator:

1 / (1953125 * (1 / 16777216)) = 1 * (16777216 / 1953125)

Thus, the expression equivalent to 5^-9 / 4^-12 with positive exponents only is:

16777216 / 1953125