Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To find the value of [tex]\( k \)[/tex] when [tex]\((3^6)^k = 3^2\)[/tex], follow these steps:
1. Understand the Problem:
We are given the equation [tex]\((3^6)^k = 3^2\)[/tex] and need to solve for [tex]\( k \)[/tex].
2. Apply the Exponentiation Rule:
The problem involves exponents, so we use the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. Applying this rule to our equation:
[tex]\[ (3^6)^k = 3^{6k} \][/tex]
Therefore, the original equation [tex]\((3^6)^k = 3^2\)[/tex] can be rewritten as:
[tex]\[ 3^{6k} = 3^2 \][/tex]
3. Equate the Exponents:
Since the bases on both sides of the equation are the same (both are 3), we can set the exponents equal to each other:
[tex]\[ 6k = 2 \][/tex]
4. Solve for [tex]\( k \)[/tex]:
To find the value of [tex]\( k \)[/tex], solve the equation [tex]\( 6k = 2 \)[/tex] by isolating [tex]\( k \)[/tex]:
[tex]\[ k = \frac{2}{6} \][/tex]
Simplify the fraction:
[tex]\[ k = \frac{1}{3} \][/tex]
So, the value of [tex]\( k \)[/tex] is [tex]\(\boxed{0.3333333333333333}\)[/tex].
1. Understand the Problem:
We are given the equation [tex]\((3^6)^k = 3^2\)[/tex] and need to solve for [tex]\( k \)[/tex].
2. Apply the Exponentiation Rule:
The problem involves exponents, so we use the property of exponents [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]. Applying this rule to our equation:
[tex]\[ (3^6)^k = 3^{6k} \][/tex]
Therefore, the original equation [tex]\((3^6)^k = 3^2\)[/tex] can be rewritten as:
[tex]\[ 3^{6k} = 3^2 \][/tex]
3. Equate the Exponents:
Since the bases on both sides of the equation are the same (both are 3), we can set the exponents equal to each other:
[tex]\[ 6k = 2 \][/tex]
4. Solve for [tex]\( k \)[/tex]:
To find the value of [tex]\( k \)[/tex], solve the equation [tex]\( 6k = 2 \)[/tex] by isolating [tex]\( k \)[/tex]:
[tex]\[ k = \frac{2}{6} \][/tex]
Simplify the fraction:
[tex]\[ k = \frac{1}{3} \][/tex]
So, the value of [tex]\( k \)[/tex] is [tex]\(\boxed{0.3333333333333333}\)[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.