Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7 3. 7 5 with positive exponents only. (1 point)
The Property of Negative Integer Exponents states that for any nonzero real number a and any negative integer n, \(a^{-n} = \frac{1}{a^n}\).
Therefore, to rewrite \(7^3 \cdot 7^5\) with positive exponents only, we can use the property to convert the negative exponent to a positive exponent:
\(7^3 \cdot 7^5 = 7^{3+5} = 7^8\)
So the expression equivalent to \(7^3 \cdot 7^5\) with positive exponents only is \(7^8\).
That’s wrong
Apologies for the incorrect response.
To apply the Property of Negative Integer Exponents to generate an expression equivalent to \(7^3 \cdot 7^5\) with positive exponents only, we can use the property of the product of powers:
\(a^m \cdot a^n = a^{m+n}\)
Using this property, we can combine the exponents:
\(7^3 \cdot 7^5 = 7^{3+5} = 7^8\)
So the expression equivalent to \(7^3 \cdot 7^5\) with positive exponents only is \(7^8\).
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7 -3. 7 -5 with positive exponents only. (1 point)
The Property of Negative Integer Exponents states that for any nonzero real number a and any negative integer n, \(a^{-n} = \frac{1}{a^n}\).
To generate an expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only, we can use the property to convert the negative exponents to positive exponents:
\(7^{-3} \cdot 7^{-5} = \frac{1}{7^3} \cdot \frac{1}{7^5} = \frac{1}{7^3 \cdot 7^5} = \frac{1}{7^{3+5}} = \frac{1}{7^8}\)
So the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(\frac{1}{7^8}\).
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^-9/4^-12 with positive exponents
only. (1 point)
To apply the Property of Negative Integer Exponents to generate an expression equivalent to \(5^{-9} \div 4^{-12}\) with positive exponents only, we can use the property of division of powers:
\[a^m \div a^n = a^{m-n}\]
Using this property, we can rewrite the expression:
\[5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{4^{12}}{5^9}\]
To simplify this further, we can also use the property of negative exponents:
\(\frac{4^{12}}{5^9} = \frac{4^{12}}{5^9} \cdot \frac{5^3}{5^3}\)
Now, we can apply the property of power of a power:
\(\frac{4^{12}}{5^9} \cdot \frac{5^3}{5^3} = \frac{4^{12} \cdot 5^3}{5^3 \cdot 5^9} = \frac{4^{12} \cdot 5^3}{5^{3 + 9}} = \frac{4^{12} \cdot 5^3}{5^{12}}\)
Finally, we can rewrite the expression with positive exponents:
\(\frac{4^{12} \cdot 5^3}{5^{12}} = \frac{4^{12}}{5^{12}} \cdot \frac{5^3}{1} = \left(\frac{4}{5}\right)^{12} \cdot 5^3 = \frac{64}{3125}\)
So, the expression equivalent to \(5^{-9} \div 4^{-12}\) with positive exponents only is \(\frac{64}{3125}\).
That’s wrong.
Apologies for the incorrect response.
To apply the Property of Negative Integer Exponents to generate an expression equivalent to \(5^{-9} \div 4^{-12}\) with positive exponents only, we can use the property of division of powers:
\(a^m \div a^n = a^{m-n}\)
Using this property, we can rewrite the expression:
\(5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}}\)
Now, let's apply the property of negative exponents:
\(\frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{1}{5^9} \cdot 4^{12}\)
We can simplify further by expressing \(4^{12}\) as \((2^2)^{12} = 2^{2 \cdot 12} = 2^{24}\):
\(\frac{1}{5^9} \cdot 4^{12} = \frac{1}{5^9} \cdot 2^{24}\)
Now, let's rewrite \(2^{24}\) as \((2^3)^8 = 8^8\):
\(\frac{1}{5^9} \cdot 2^{24} = \frac{1}{5^9} \cdot 8^8\)
Finally, we can rewrite the expression with positive exponents:
\(\frac{1}{5^9} \cdot 8^8 = \left(\frac{8}{5^9}\right)^8\)
So, the expression equivalent to \(5^{-9} \div 4^{-12}\) with positive exponents only is \(\left(\frac{8}{5^9}\right)^8\).