Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12 with positive exponents only.
To apply the property of negative integer exponents, we can rewrite the expression as:
1/(5^9)/(4^12)
Now, let's simplify this expression by converting the bases to positive exponents:
= (1/5^9)/(1/4^12)
Next, we can use the property of division to simplify further:
= (1/5^9) * (4^12/1)
= (4^12)/(5^9)
Therefore, the expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^12)/(5^9).
To generate an expression equivalent to 5^(-9)/4^(-12) with positive exponents only, we can apply the Property of Negative Integer Exponents:
For any non-zero number a and positive integer n, a^(-n) can be written as 1/a^n.
Using this property, we can rewrite the expression as:
5^(-9)/4^(-12) = 1/(5^9)/(1/(4^12))
Now, we can simplify further:
1/(5^9)/(1/(4^12)) = (4^12)/(5^9)
Therefore, the expression equivalent to 5^(-9)/4^(-12) with positive exponents only is (4^12)/(5^9).
To generate an expression with positive exponents only, we can apply the property of negative integer exponents which states that any nonzero number raised to a negative exponent is equal to the reciprocal of that number raised to the positive exponent.
In this case, we have the expression 5^(-9) / 4^(-12). We can apply the property by reciprocating both the numerator and the denominator:
1 / (5^9 / 4^12)
Next, we can simplify this expression by multiplying the numerator by the denominator's reciprocal.
1 * (4^12 / 5^9)
Finally, to simplify further, we can rewrite 4^12 as (2^2)^12, and 5^9 as (5^2)^4 * 5.
1 * ((2^2)^12 / (5^2)^4 * 5)
Simplifying the exponents, we have:
1 * (2^24 / 5^8 * 5)
Now, we can multiply 5^8 by 5:
1 * (2^24 / 5^8 * 5^1)
Since the bases are the same, we can combine the exponents in the denominator:
1 * (2^24 / 5^(8+1))
Simplifying further:
1 * (2^24 / 5^9)
Thus, the expression equivalent to 5^(-9) / 4^(-12) with positive exponents only is 2^24 / 5^9.