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Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7−3⋅7−5 with positive exponents only.(...Asked by Food
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7 3. 7 5 with positive exponents only. (1 point)
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Answered by
Food
That’s wrong
Answered by
Food
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7 -3. 7 -5 with positive exponents only. (1 point)
Answered by
Food
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^-9/4^-12 with positive exponents
only. (1 point)
only. (1 point)
Answered by
Food
That’s wrong.
Answered by
Food
Still wrong.
Answered by
Food
So what does it equal?
Answered by
GPT 3.5
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 \(7^8\).
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 \(7^8\).
Answered by
GPT 3.5
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 \(7^8\).
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 \(7^8\).
Answered by
GPT 3.5
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 \(\frac{1}{7^8}\).
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 \(\frac{1}{7^8}\).
Answered by
GPT 3.5
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 \(\frac{64}{3125}\).
\[a^m \div a^n = a^{m-n}\]
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 \(\frac{64}{3125}\).
Answered by
GPT 3.5
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 \(\left(\frac{8}{5^9}\right)^8\).
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 \(\left(\frac{8}{5^9}\right)^8\).
Answered by
GPT 3.5
Apologies for the confusion. Let's try again.
To apply the Property of Negative Integer Exponents, we have:
\[5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}}\]
Now, let's simplify each base:
\(\frac{1}{5^9} = 5^{-9}\)
\(\frac{1}{4^{12}} = 4^{-12}\)
Now, using the Property of Negative Integer Exponents, we can rewrite each term:
\[5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{1}{5^{-9}} \times \frac{1}{4^{-12}}\]
Using the Property of Division of Powers, we can combine the exponents:
\[\frac{1}{5^{-9}} \times \frac{1}{4^{-12}} = 5^9 \times 4^{12}\]
Therefore, the expression equivalent to \(5^{-9} \div 4^{-12}\) with positive exponents only is \(5^9 \times 4^{12}\).
To apply the Property of Negative Integer Exponents, we have:
\[5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}}\]
Now, let's simplify each base:
\(\frac{1}{5^9} = 5^{-9}\)
\(\frac{1}{4^{12}} = 4^{-12}\)
Now, using the Property of Negative Integer Exponents, we can rewrite each term:
\[5^{-9} \div 4^{-12} = \frac{1}{5^9} \div \frac{1}{4^{12}} = \frac{1}{5^{-9}} \times \frac{1}{4^{-12}}\]
Using the Property of Division of Powers, we can combine the exponents:
\[\frac{1}{5^{-9}} \times \frac{1}{4^{-12}} = 5^9 \times 4^{12}\]
Therefore, the expression equivalent to \(5^{-9} \div 4^{-12}\) with positive exponents only is \(5^9 \times 4^{12}\).
Answered by
GPT 3.5
My apologies for the confusion. Let's simplify the expression further:
\(5^9 \times 4^{12}\)
To simplify this expression, we can calculate each base raised to its exponent:
\(5^9 = 195,3125\) (approximately)
\(4^{12} = 16,777,216\)
Now, we can multiply these values:
\(195,3125 \times 16,777,216 = 3,280,558,740,000\)
Therefore, the expression \(5^{-9} \div 4^{-12}\) is equivalent to approximately \(3,280,558,740,000\) with positive exponents only.
\(5^9 \times 4^{12}\)
To simplify this expression, we can calculate each base raised to its exponent:
\(5^9 = 195,3125\) (approximately)
\(4^{12} = 16,777,216\)
Now, we can multiply these values:
\(195,3125 \times 16,777,216 = 3,280,558,740,000\)
Therefore, the expression \(5^{-9} \div 4^{-12}\) is equivalent to approximately \(3,280,558,740,000\) with positive exponents only.