1) Apply the Property of Negative Integer Exponents to rewrite 15^−38 as an expression with positive exponents only.
2) Apply the Property of Negative Integer Exponents to rewrite 9^−23 as an expression with positive exponents only.
3) Apply the Property of Negative Integer Exponents to solve 3^−4. The answer should not contain any exponent expression or decimals.
4) Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3 x 7^−5 with positive exponents only.
5) Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9 / 4^−12 with positive exponents only. (The "/" is supposed to represent a fraction)
1) To apply the Property of Negative Integer Exponents, we can rewrite 15^-38 as 1/15^38.
2) Similarly, we can rewrite 9^-23 as 1/9^23.
3) To solve 3^-4 using the Property of Negative Integer Exponents, we can write it as 1/3^4, which simplifies to 1/81.
4) To generate an expression equivalent to 7^-3 x 7^-5 with positive exponents only, we can use the Product of Powers Property. This allows us to add the exponents together, giving us 7^-3 x 7^-5 = 7^-8.
5) To generate an expression equivalent to 5^-9 / 4^-12 with positive exponents only, we can use the Quotient of Powers Property. This property allows us to subtract the exponents, giving us 5^-9 / 4^-12 = 5^-9 x 4^12.
#4 and #5 are wrong
Apologies for the mistake. Let's correct the answers for #4 and #5.
4) To generate an expression equivalent to 7^-3 x 7^-5 with positive exponents only, we can again use the Product of Powers Property. This property states that when multiplying expressions with the same base, we add the exponents. So, 7^-3 x 7^-5 can be rewritten as 7^-3+(-5) = 7^-8.
5) To generate an expression equivalent to 5^-9 / 4^-12 with positive exponents only, we can use the Quotient of Powers Property. This property states that when dividing expressions with the same base, we subtract the exponents. So, 5^-9 / 4^-12 can be rewritten as 5^-9 / 4^-12 = 5^-9 x 4^12.
1) To rewrite 15^−38 with positive exponents, we can apply the Property of Negative Integer Exponents, which states that a^(−n) = 1/(a^n). Therefore, 15^−38 can be expressed as 1/(15^38).
2) Similarly, to rewrite 9^−23 with positive exponents, we can apply the Property of Negative Integer Exponents. So, 9^−23 becomes 1/(9^23).
3) To solve 3^−4 using the Property of Negative Integer Exponents, we can rewrite it as 1/(3^4). Therefore, the answer is 1/81.
4) To generate an expression equivalent to 7^−3 x 7^−5 with positive exponents only, we can apply the Property of Negative Integer Exponents, which states that a^(−n) = 1/(a^n). Therefore, 7^−3 x 7^−5 can be expressed as (1/7^3) x (1/7^5).
5) Finally, to generate an expression equivalent to 5^−9 / 4^−12 with positive exponents only, we can again apply the Property of Negative Integer Exponents. So, 5^−9 / 4^−12 becomes (1/5^9) / (1/4^12), which is equivalent to (4^12) / (5^9).
1) To rewrite 15^−38 with positive exponents only using the property of negative exponents, we can apply the rule that says: a^−n = 1 / a^n.
So, 15^−38 can be rewritten as 1 / 15^38.
2) Similarly, to rewrite 9^−23 with positive exponents only using the property of negative exponents, we apply the same rule: a^−n = 1 / a^n.
Therefore, 9^−23 can be rewritten as 1 / 9^23.
3) To solve 3^−4 using the property of negative exponents, we also apply the rule a^−n = 1 / a^n.
Thus, 3^−4 can be simplified as 1 / 3^4 = 1 / 81.
4) When generating an expression equivalent to 7^−3 x 7^−5 with positive exponents only, we can use the rule that states a^m x a^n = a^(m + n).
Applying this rule, 7^−3 x 7^−5 becomes 7^(-3 + -5) = 7^(-8).
To rewrite it with a positive exponent, we use the rule a^−n = 1 / a^n.
Therefore, 7^(-8) = 1 / 7^8.
5) For generating an expression equivalent to 5^−9 / 4^−12, we can use the rule a^−n = 1 / a^n.
Hence, 5^−9 / 4^−12 becomes 1 / 5^9 x 1 / 4^12.
Applying the rule a^m x a^n = a^(m + n), we can simplify this expression as 1 / (5^9 x 4^12).