Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5−94−12 with positive exponents only.
To apply the Property of Negative Integer Exponents, we know that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent.
So, for 5^(-9), we can rewrite it as 1/(5^9) because when we switch the sign of the exponent, it becomes the reciprocal of the number raised to the positive exponent.
Similarly, for 4^(-12), we can rewrite it as 1/(4^12).
Combining both of these, the expression 5^(-9) * 4^(-12) can be written as:
1/(5^9) * 1/(4^12)
This expression is equivalent to 5^(-9) * 4^(-12) with positive exponents only.
To apply the property of negative integer exponents to generate an expression with positive exponents, we can use the fact that any non-zero number raised to the power of a negative exponent is equal to its reciprocal raised to the positive exponent.
The expression 5⁻⁹⁴⁻¹² can be rewritten as:
1/(5⁹⁴ × 5¹²)
Using the property of negative exponents, we can rewrite this as:
1/(5⁹⁴ × 1/5¹²)
Simplifying further by multiplying the numerator and denominator by the reciprocal of 1/5¹² (which is 5¹²), we get:
5¹²/(5⁹⁴ × 1)
Finally, simplifying further, we have:
5¹²/5⁹⁴
Therefore, the expression equivalent to 5⁻⁹⁴⁻¹² with positive exponents only is 5¹²/5⁹⁴.
To apply the property of negative integer exponents, we use the fact that for any non-zero number a and any negative integer n, a^(-n) is equal to 1 divided by a^n.
In this case, we have 5^(-9) * 4^(-12). Following the property of negative exponents, we can rewrite this expression with positive exponents only.
Step 1: Reciprocal of 5^(-9)
Reciprocal means inverting a number. So, 5^(-9) can be written as 1/(5^9).
Step 2: Reciprocal of 4^(-12)
Similarly, 4^(-12) can be written as 1/(4^12).
Now, our expression becomes:
1/(5^9) * 1/(4^12)
Simplifying further, we can combine the two fractions by multiplying the numerators and denominators:
1 / (5^9 * 4^12)
And that is the expression equivalent to 5^(-9) * 4^(-12) with positive exponents only.