I'll probably the property of negative integer exponents to generate an expression equivalent to 2 ^ -13 over 5 ^ -12 with positive exponents only.
To convert the expression 2^-13 / 5^-12 into an expression with positive exponents only, we can make use of the property of negative exponents which states: a^-n = 1 / a^n.
Therefore, we can rewrite the expression as follows:
2^-13 / 5^-12 = (1 / 2^13) / (1 / 5^12)
Now, to divide by a fraction, we can multiply by its reciprocal:
(1 / 2^13) / (1 / 5^12) = (1 / 2^13) * (5^12 / 1)
Now, applying the rule of exponents for multiplication, which states: a^m * a^n = a^(m + n), we can simplify the expression:
(1 / 2^13) * (5^12 / 1) = (5^12) / (2^13)
Therefore, the expression equivalent to 2^-13 / 5^-12 with positive exponents only is (5^12) / (2^13).
To express the given expression with positive exponents only, you can use the property of negative exponents, which states that a^-n is equal to 1/a^n.
Let's apply this property to the given expression:
2^-13 over 5^-12
Using the property of negative exponents, we can rewrite this expression as:
(1/2^13) over (1/5^12)
When dividing fractions, we can multiply the numerator by the reciprocal of the denominator. Applying this, we get:
(1/2^13) * (5^12/1)
Simplifying further, we have:
5^12/2^13
Therefore, the expression 2^-13 over 5^-12 is equivalent to 5^12/2^13 with positive exponents only.