The correct expression developed using the product rule of exponents is:
\(x^{a} \cdot x^{b} = x^{a+b}\)
which expression is correctly developed to use the product rules of exponents
27 answers
find the numerical equivalent of 10^(2) 10^(3)
To find the numerical equivalent of \(10^2 \cdot 10^3\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).
Using this rule, we can simplify the expression as follows:
\(10^2 \cdot 10^3 = 10^{2+3} = 10^5\)
Therefore, \(10^2 \cdot 10^3\) is equal to \(10^5\), which is equal to 100,000.
Using this rule, we can simplify the expression as follows:
\(10^2 \cdot 10^3 = 10^{2+3} = 10^5\)
Therefore, \(10^2 \cdot 10^3\) is equal to \(10^5\), which is equal to 100,000.
which of the following correctly use the product rule of exponents to simplify the expression 100^(8) 100^(7)
To simplify the expression \(100^8 \cdot 100^7\), we can use the product rule of exponents: \(a^m \cdot a^n = a^{m+n}\).
Using this rule, we can simplify the expression as follows:
\(100^8 \cdot 100^7 = 100^{8+7} = 100^{15}\)
Therefore, the correct expression using the product rule of exponents to simplify the expression is \(100^{8+7}\).
Using this rule, we can simplify the expression as follows:
\(100^8 \cdot 100^7 = 100^{8+7} = 100^{15}\)
Therefore, the correct expression using the product rule of exponents to simplify the expression is \(100^{8+7}\).
Find the numerical equivalent of 2^(5) 2^(-2)
To find the numerical equivalent of \(2^5 \cdot 2^{-2}\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).
Using this rule, we can simplify the expression as follows:
\(2^5 \cdot 2^{-2} = 2^{5 + (-2)} = 2^3\)
Therefore, \(2^5 \cdot 2^{-2}\) is equal to \(2^3\), which equals 8.
Using this rule, we can simplify the expression as follows:
\(2^5 \cdot 2^{-2} = 2^{5 + (-2)} = 2^3\)
Therefore, \(2^5 \cdot 2^{-2}\) is equal to \(2^3\), which equals 8.
Find the numerical equivalent 10^(9) 10^(-7)
To find the numerical equivalent of \(10^9 \cdot 10^{-7}\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).
Using this rule, we can simplify the expression as follows:
\(10^9 \cdot 10^{-7} = 10^{9 + (-7)} = 10^2\)
Therefore, \(10^9 \cdot 10^{-7}\) is equal to \(10^2\), which equals 100.
Using this rule, we can simplify the expression as follows:
\(10^9 \cdot 10^{-7} = 10^{9 + (-7)} = 10^2\)
Therefore, \(10^9 \cdot 10^{-7}\) is equal to \(10^2\), which equals 100.
Find the numerical equivalent of 4^(9) 4^(-7)
To find the numerical equivalent of \(4^9 \cdot 4^{-7}\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).
Using this rule, we can simplify the expression as follows:
\(4^9 \cdot 4^{-7} = 4^{9 + (-7)} = 4^2\)
Therefore, \(4^9 \cdot 4^{-7}\) is equal to \(4^2\), which equals 16.
Using this rule, we can simplify the expression as follows:
\(4^9 \cdot 4^{-7} = 4^{9 + (-7)} = 4^2\)
Therefore, \(4^9 \cdot 4^{-7}\) is equal to \(4^2\), which equals 16.
which expression is correctly developed to use the product rule of exponents
10^(8) 10^(8)
32^(7)
6^(2) 7^(3)
5^((2))^9
10^(8) 10^(8)
32^(7)
6^(2) 7^(3)
5^((2))^9
The expression that is correctly developed to use the product rule of exponents is:
10^(8) 10^(8)
Using the product rule of exponents, we can simplify this expression as:
10^(8+8) = 10^(16)
10^(8) 10^(8)
Using the product rule of exponents, we can simplify this expression as:
10^(8+8) = 10^(16)
Simplify the expression using the quotient rule of integer exponents: t400/t400
t^(4)
300
t^(500)
t^(300)
t^(4)
300
t^(500)
t^(300)
To simplify the expression \(\frac{t^{400}}{t^{400}}\) using the quotient rule of exponents, we subtract the exponents:
\[t^{400-400} = t^0\]
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
\[t^0 = 1\]
\[t^{400-400} = t^0\]
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
\[t^0 = 1\]
simplify a^(67)/b^(34)
To simplify the expression \(\frac{a^{67}}{b^{34}}\) using the quotient rule of exponents, we subtract the exponents:
\(\frac{a^{67}}{b^{34}} = a^{67 - 34}\)
Simplifying the exponent, we have:
\(a^{67 - 34} = a^{33}\)
Therefore, the simplified expression is \(a^{33}\).
\(\frac{a^{67}}{b^{34}} = a^{67 - 34}\)
Simplifying the exponent, we have:
\(a^{67 - 34} = a^{33}\)
Therefore, the simplified expression is \(a^{33}\).
apply the quotient rule of integer exponents to simplify 23^(65) / 23^(32)
To simplify the expression \(\frac{23^{65}}{23^{32}}\) using the quotient rule of integer exponents, we subtract the exponents:
\(\frac{23^{65}}{23^{32}} = 23^{65 - 32}\)
Simplifying the exponent, we have:
\(23^{65 - 32} = 23^{33}\)
Therefore, the simplified expression is \(23^{33}\).
\(\frac{23^{65}}{23^{32}} = 23^{65 - 32}\)
Simplifying the exponent, we have:
\(23^{65 - 32} = 23^{33}\)
Therefore, the simplified expression is \(23^{33}\).
simplify this expression using the quotient rule of integer exponents
12^(53) / 7^(53)
12^(53) / 7^(53)
To simplify the expression \(\frac{12^{53}}{7^{53}}\) using the quotient rule of integer exponents, we subtract the exponents:
\(\frac{12^{53}}{7^{53}} = 12^{53 - 53}\)
Simplifying the exponent, we have:
\(12^{53 - 53} = 12^0\)
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
\(12^0 = 1\)
\(\frac{12^{53}}{7^{53}} = 12^{53 - 53}\)
Simplifying the exponent, we have:
\(12^{53 - 53} = 12^0\)
Any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
\(12^0 = 1\)
12^(53) / 7^(53)
To simplify the expression \(\frac{12^{53}}{7^{53}}\), we can rewrite it as a single exponent:
\(\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}\)
Therefore, the simplified expression is \(\left(\frac{12}{7}\right)^{53}\).
\(\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}\)
Therefore, the simplified expression is \(\left(\frac{12}{7}\right)^{53}\).
12^(53) divided by 7^(53)
To simplify the expression \(\frac{12^{53}}{7^{53}}\), we can use the quotient rule of exponents, which states that \(a^m \div a^n = a^{m-n}\).
Applying this rule, we subtract the exponents:
\(\frac{12^{53}}{7^{53}} = 12^{53-53} \div 7^{53-53} = 12^{0} \div 7^{0}\)
Any number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
\(12^{0} \div 7^{0} = 1 \div 1 = 1\)
Applying this rule, we subtract the exponents:
\(\frac{12^{53}}{7^{53}} = 12^{53-53} \div 7^{53-53} = 12^{0} \div 7^{0}\)
Any number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:
\(12^{0} \div 7^{0} = 1 \div 1 = 1\)
what are the correct steps to follow to simplify an exponential expression using the quotient rule of integer exponents
To simplify an exponential expression using the quotient rule of integer exponents, follow these steps:
1. Identify the base of each term in the expression.
2. Determine the exponents of each term.
3. Write the expression as a fraction, with the numerator being the term with the numerator exponent and the denominator being the term with the denominator exponent.
4. Subtract the exponents: numerator exponent minus denominator exponent.
5. Simplify the resulting fraction if possible.
6. Rewrite the expression using the simplified exponent.
For example, to simplify \(a^m / a^n\) using the quotient rule, you would:
1. Identify the base as \(a\).
2. Determine the exponents, \(m\) and \(n\).
3. Write the expression as \(a^m / a^n\).
4. Subtract the exponents: \(m - n\).
5. Simplify the resulting fraction if possible.
6. Rewrite the expression as \(a^{(m-n)}\).
1. Identify the base of each term in the expression.
2. Determine the exponents of each term.
3. Write the expression as a fraction, with the numerator being the term with the numerator exponent and the denominator being the term with the denominator exponent.
4. Subtract the exponents: numerator exponent minus denominator exponent.
5. Simplify the resulting fraction if possible.
6. Rewrite the expression using the simplified exponent.
For example, to simplify \(a^m / a^n\) using the quotient rule, you would:
1. Identify the base as \(a\).
2. Determine the exponents, \(m\) and \(n\).
3. Write the expression as \(a^m / a^n\).
4. Subtract the exponents: \(m - n\).
5. Simplify the resulting fraction if possible.
6. Rewrite the expression as \(a^{(m-n)}\).
1 answer