Discover the best answers to your questions with the help of IDNLearn.com. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.
Sagot :
To simplify the expression \(\left(5^3\right)^2\) and rewrite it in the form \(5^n\), we will follow a detailed, step-by-step approach.
1. Understand the Expression:
\(\left(5^3\right)^2\) means that we are raising \(5^3\) to the power of 2.
2. Apply the Power of a Power Rule:
The power of a power rule states that \((a^m)^n = a^{m \cdot n}\). Here, \(a = 5\), \(m = 3\), and \(n = 2\).
3. Multiply the Exponents:
Following the rule \((a^m)^n = a^{m \cdot n}\), we have:
[tex]\[ (5^3)^2 = 5^{3 \cdot 2} \][/tex]
Calculate the multiplication of the exponents:
[tex]\[ 3 \cdot 2 = 6 \][/tex]
4. Rewrite the Expression:
Replace the exponent with the calculated value:
[tex]\[ (5^3)^2 = 5^6 \][/tex]
So, the simplified form of the expression \(\left(5^3\right)^2\) rewritten in the form \(5^n\) is \(5^6\).
To express the value:
[tex]\[ 5^6 = 15625 \][/tex]
Final answer:
[tex]\[ \left(5^3\right)^2 = 5^6 = 15625 \][/tex]
1. Understand the Expression:
\(\left(5^3\right)^2\) means that we are raising \(5^3\) to the power of 2.
2. Apply the Power of a Power Rule:
The power of a power rule states that \((a^m)^n = a^{m \cdot n}\). Here, \(a = 5\), \(m = 3\), and \(n = 2\).
3. Multiply the Exponents:
Following the rule \((a^m)^n = a^{m \cdot n}\), we have:
[tex]\[ (5^3)^2 = 5^{3 \cdot 2} \][/tex]
Calculate the multiplication of the exponents:
[tex]\[ 3 \cdot 2 = 6 \][/tex]
4. Rewrite the Expression:
Replace the exponent with the calculated value:
[tex]\[ (5^3)^2 = 5^6 \][/tex]
So, the simplified form of the expression \(\left(5^3\right)^2\) rewritten in the form \(5^n\) is \(5^6\).
To express the value:
[tex]\[ 5^6 = 15625 \][/tex]
Final answer:
[tex]\[ \left(5^3\right)^2 = 5^6 = 15625 \][/tex]
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.