Answer :
To simplify the expression \(\frac{3^{10}}{3^4}\), you should use the quotient of powers property. This property states that for any non-zero base \(a\) and any integers \(m\) and \(n\):
[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]
Here's a detailed step-by-step solution applying this property:
1. Identify the base and the exponents in the given expression. The base is 3, \(m\) (the exponent in the numerator) is 10, and \(n\) (the exponent in the numerator) is 4.
2. Apply the quotient of powers property to the expression:
[tex]\[ \frac{3^{10}}{3^4} = 3^{10-4} \][/tex]
3. Subtract the exponents:
[tex]\[ 10 - 4 = 6 \][/tex]
4. Simplify the expression to:
[tex]\[ 3^6 \][/tex]
Therefore, \(\frac{3^{10}}{3^4}\) simplifies to \(3^6\).
5. Finally, calculate \(3^6\):
[tex]\[ 3^6 = 729 \][/tex]
So, the simplified form of the expression [tex]\(\frac{3^{10}}{3^4}\)[/tex] is [tex]\(729\)[/tex].
[tex]\[ \frac{a^m}{a^n} = a^{m-n} \][/tex]
Here's a detailed step-by-step solution applying this property:
1. Identify the base and the exponents in the given expression. The base is 3, \(m\) (the exponent in the numerator) is 10, and \(n\) (the exponent in the numerator) is 4.
2. Apply the quotient of powers property to the expression:
[tex]\[ \frac{3^{10}}{3^4} = 3^{10-4} \][/tex]
3. Subtract the exponents:
[tex]\[ 10 - 4 = 6 \][/tex]
4. Simplify the expression to:
[tex]\[ 3^6 \][/tex]
Therefore, \(\frac{3^{10}}{3^4}\) simplifies to \(3^6\).
5. Finally, calculate \(3^6\):
[tex]\[ 3^6 = 729 \][/tex]
So, the simplified form of the expression [tex]\(\frac{3^{10}}{3^4}\)[/tex] is [tex]\(729\)[/tex].
