To apply the Property of Negative Integer Exponents, we know that for any non-zero number a,
\[a^{-n} = \dfrac{1}{a^n}\]
Therefore, we can rewrite the expression \(7^{-3} \cdot 7^{-5}\) as:
\[7^{-3} \cdot 7^{-5} = \dfrac{1}{7^3} \cdot \dfrac{1}{7^5}\]
To simplify this expression further, we use the Property of Product of Powers, which states that for any non-zero number a, and any integers m and n,
\[a^m \cdot a^n = a^{m+n}\]
Applying this property, we can combine the two fractions:
\[\dfrac{1}{7^3} \cdot \dfrac{1}{7^5} = \dfrac{1}{7^{(3+5)}} = \dfrac{1}{7^8}\]
So, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(\dfrac{1}{7^8}\).
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only.
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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.
7^−3⋅7^−5=
7^−3⋅7^−5=
To apply the Property of Negative Integer Exponents, we know that for any non-zero number a,
\[a^{-n} = \dfrac{1}{a^n}\]
Using this property, we can rewrite \(7^{-3} \cdot 7^{-5}\) as:
\[7^{-3} \cdot 7^{-5} = \dfrac{1}{7^3} \cdot \dfrac{1}{7^5}\]
Now, let's simplify these fractions by multiplying the numerators and denominators:
\[\dfrac{1}{7^3} \cdot \dfrac{1}{7^5} = \dfrac{1 \cdot 1}{7^3 \cdot 7^5} = \dfrac{1}{7^{3 + 5}}\]
Simplifying the exponent by adding:
\[\dfrac{1}{7^{3 + 5}} = \dfrac{1}{7^8}\]
Therefore, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(\dfrac{1}{7^8}\).
\[a^{-n} = \dfrac{1}{a^n}\]
Using this property, we can rewrite \(7^{-3} \cdot 7^{-5}\) as:
\[7^{-3} \cdot 7^{-5} = \dfrac{1}{7^3} \cdot \dfrac{1}{7^5}\]
Now, let's simplify these fractions by multiplying the numerators and denominators:
\[\dfrac{1}{7^3} \cdot \dfrac{1}{7^5} = \dfrac{1 \cdot 1}{7^3 \cdot 7^5} = \dfrac{1}{7^{3 + 5}}\]
Simplifying the exponent by adding:
\[\dfrac{1}{7^{3 + 5}} = \dfrac{1}{7^8}\]
Therefore, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(\dfrac{1}{7^8}\).
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only.
7^−3⋅7^−5=
7^−3⋅7^−5=
To generate an expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only, we can apply the Property of Negative Integer Exponents, which states that for any non-zero number \(a\), \(a^{-n} = \dfrac{1}{a^n}\).
Using this property, we can rewrite \(7^{-3} \cdot 7^{-5}\) as:
\(7^{-3} \cdot 7^{-5} = \dfrac{1}{7^3} \cdot \dfrac{1}{7^5}\)
Next, let's simplify these fractions by multiplying the numerators and denominators:
\(\dfrac{1}{7^3} \cdot \dfrac{1}{7^5} = \dfrac{1 \cdot 1}{7^3 \cdot 7^5} = \dfrac{1}{7^{3+5}}\)
Simplifying the exponent by adding:
\(\dfrac{1}{7^{3+5}} = \dfrac{1}{7^8}\)
Therefore, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(\dfrac{1}{7^8}\).
Using this property, we can rewrite \(7^{-3} \cdot 7^{-5}\) as:
\(7^{-3} \cdot 7^{-5} = \dfrac{1}{7^3} \cdot \dfrac{1}{7^5}\)
Next, let's simplify these fractions by multiplying the numerators and denominators:
\(\dfrac{1}{7^3} \cdot \dfrac{1}{7^5} = \dfrac{1 \cdot 1}{7^3 \cdot 7^5} = \dfrac{1}{7^{3+5}}\)
Simplifying the exponent by adding:
\(\dfrac{1}{7^{3+5}} = \dfrac{1}{7^8}\)
Therefore, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(\dfrac{1}{7^8}\).
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3 ⋅ 7^−5 with positive exponents only. (1 point)
7^−3 ⋅ 7^−5 =
7^−3 ⋅ 7^−5 =
To apply the Property of Negative Integer Exponents, we can multiply the exponents and apply the negative sign to the result. So, for \(7^{-3} \cdot 7^{-5}\), we have:
\(7^{-3} \cdot 7^{-5} = 7^{-3-5}\)
Now we can simplify the exponents:
\(7^{-3-5} = 7^{-8}\)
Therefore, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(7^{-8}\).
\(7^{-3} \cdot 7^{-5} = 7^{-3-5}\)
Now we can simplify the exponents:
\(7^{-3-5} = 7^{-8}\)
Therefore, 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)
7^−3 * 7^−5 =
7^−3 * 7^−5 =
To apply the Property of Negative Integer Exponents, we can combine the two negative exponents by adding them. So for \(7^{-3} \cdot 7^{-5}\), we have:
\(7^{-3} \cdot 7^{-5} = 7^{-3-5}\)
Simplifying the exponent, we get:
\(7^{-3-5} = 7^{-8}\)
Therefore, the expression equivalent to \(7^{-3} \cdot 7^{-5}\) with positive exponents only is \(7^{-8}\).
\(7^{-3} \cdot 7^{-5} = 7^{-3-5}\)
Simplifying the exponent, we get:
\(7^{-3-5} = 7^{-8}\)
Therefore, 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 5^−9/4^−12 with positive exponents only.
To apply the Property of Negative Integer Exponents, we can rewrite the given expression as:
\(\dfrac{1}{5^9} \cdot \dfrac{1}{4^{-12}}\)
Now, let's simplify these fractions using the Property of Negative Integer Exponents:
\(\dfrac{1}{5^9} \cdot \dfrac{1}{4^{-12}} = \dfrac{1}{5^9} \cdot 4^{12}\)
To simplify further, we can rewrite \(4^{12}\) as \((2^2)^{12}\):
\(\dfrac{1}{5^9} \cdot 4^{12} = \dfrac{1}{5^9} \cdot (2^2)^{12} = \dfrac{1}{5^9} \cdot 2^{24}\)
Now, we use the Property of Product of Powers to combine the two bases with the same exponent:
\(\dfrac{1}{5^9} \cdot 2^{24} = \dfrac{2^{24}}{5^9}\)
Therefore, the expression equivalent to \(5^{-9} \cdot 4^{-12}\) with positive exponents only is \(\dfrac{2^{24}}{5^9}\).
\(\dfrac{1}{5^9} \cdot \dfrac{1}{4^{-12}}\)
Now, let's simplify these fractions using the Property of Negative Integer Exponents:
\(\dfrac{1}{5^9} \cdot \dfrac{1}{4^{-12}} = \dfrac{1}{5^9} \cdot 4^{12}\)
To simplify further, we can rewrite \(4^{12}\) as \((2^2)^{12}\):
\(\dfrac{1}{5^9} \cdot 4^{12} = \dfrac{1}{5^9} \cdot (2^2)^{12} = \dfrac{1}{5^9} \cdot 2^{24}\)
Now, we use the Property of Product of Powers to combine the two bases with the same exponent:
\(\dfrac{1}{5^9} \cdot 2^{24} = \dfrac{2^{24}}{5^9}\)
Therefore, the expression equivalent to \(5^{-9} \cdot 4^{-12}\) with positive exponents only is \(\dfrac{2^{24}}{5^9}\).
1 answer