To simplify the expression [tex]\(\frac{3^{10}}{3^4}\)[/tex], you would use the quotient of powers rule. This rule states that when you divide two exponential expressions with the same base, you subtract the exponents.
Here's the step-by-step solution:
1. Identify the base and exponents:
- The base in both the numerator and the denominator is 3.
- The exponent in the numerator is 10.
- The exponent in the denominator is 4.
2. Apply the quotient of powers rule:
- According to the quotient of powers rule, [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex], where [tex]\(a\)[/tex] is the base and [tex]\(m\)[/tex] and [tex]\(n\)[/tex] are the exponents.
3. Subtract the exponents:
[tex]\[
\frac{3^{10}}{3^4} = 3^{10-4}
\][/tex]
4. Simplify the exponent:
[tex]\[
3^{10-4} = 3^6
\][/tex]
5. Evaluate the simplified expression:
To find the value of [tex]\(3^6\)[/tex]:
[tex]\[
3^6 = 729
\][/tex]
Hence, the simplified expression [tex]\(\frac{3^{10}}{3^4}\)[/tex] equals 729.
The law used here is the quotient of powers rule.
