Discover the best answers to your questions with the help of IDNLearn.com. Get the information you need from our community of experts, who provide detailed and trustworthy answers.
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]
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.