Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^-9/4^-12 with only positive exponents.
To convert the expression 5^-9/4^-12 into an expression with only positive exponents, we can apply the property of negative integer exponents, which states that a^(-b) is equal to 1/a^b.
Using this property, we can rewrite 5^-9 as 1/5^9 and 4^-12 as 1/4^12. Therefore, the expression becomes:
(1/5^9)/(1/4^12)
Next, we can simplify this expression further by multiplying the numerator and denominator by the reciprocal of the denominator, which is 4^12. This reciprocal is equivalent to 1/4^12, so we have:
(1/5^9) * (4^12/1)
Now, we multiply the numerators and denominators separately:
(1 * 4^12) / (5^9 * 1)
This simplifies to:
4^12 / 5^9
Hence, the expression equivalent to 5^-9/4^-12 with only positive exponents is 4^12 / 5^9.
To apply the Property of Negative Integer Exponents, we can rewrite the expression 5^(-9) / 4^(-12) with only positive exponents.
According to the property, we can convert a negative exponent to a positive exponent by taking the reciprocal of the base.
So, for the numerator 5^(-9), we can rewrite it as 1 / 5^9, and for the denominator 4^(-12), we can rewrite it as 1 / 4^12.
Therefore, the expression 5^(-9) / 4^(-12) is equivalent to (1 / 5^9) / (1 / 4^12).
Now, let's simplify further. To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction.
(1 / 5^9) / (1 / 4^12) can be simplified to (1 / 5^9) * (4^12 / 1).
Applying the property of exponents, where (a / b)^n = a^n / b^n, we can rewrite this as 1/(5^9) * (4^12) / 1.
Simplifying further, we get (4^12) / (5^9).
Therefore, the expression equivalent to 5^-9 / 4^-12 with only positive exponents is (4^12) / (5^9).
To apply the property of negative integer exponents, remember that when a base with a negative exponent is moved to the denominator, the sign of the exponent changes to positive. Conversely, if a base with a positive exponent is moved to the denominator, the sign of the exponent changes to negative.
Let's simplify the expression step by step:
1. Start with the expression 5^(-9) / 4^(-12).
2. Apply the property of negative exponents to move the bases to the opposite side of the fraction:
4^(12) / 5^(9).
3. Now we need to further simplify the expression by applying the property of exponents with a common base.
Since both bases are different, we can't simplify further.
4. The final equivalent expression with only positive exponents is: 4^12 / 5^9.
So, the expression equivalent to 5^(-9) / 4^(-12) with only positive exponents is 4^12 / 5^9.