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
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
To apply the property of negative integer exponents, we can rewrite the expression 5^(-9) / 4^(-12) with positive exponents by moving the bases to the opposite side of the fraction and changing the exponents to positive values.
First, let's rewrite the expression by moving 5 and 4 to the opposite sides of the fraction:
4^(-12) / 5^(-9)
Next, we can apply the property of negative exponents to obtain positive exponents:
(1 / 4^(12)) / (1 / 5^(9))
Now, we can simplify the expression by multiplying the numerator (top) and denominator (bottom) by the reciprocal of the fraction in the denominator:
(1 / 4^(12)) * (5^(9) / 1)
This can be further simplified as follows:
5^(9) / 4^(12)
Therefore, the expression equivalent to 5^(-9) / 4^(-12) with positive exponents only is 5^(9) / 4^(12).