Discover new perspectives and gain insights with IDNLearn.com's diverse answers. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.
Sagot :
Certainly! Let's write [tex]\( \left(3^6 \times 3^5\right) \div 3^7 \)[/tex] in the form [tex]\( n:1 \)[/tex], where [tex]\( n \)[/tex] is an integer.
To do this, we will use the properties of exponents. Specifically, we will use the property that states [tex]\( a^m \times a^n = a^{m+n} \)[/tex] and the property that [tex]\( \frac{a^m}{a^n} = a^{m-n} \)[/tex].
1. Combine the product of the exponents:
[tex]\[ 3^6 \times 3^5 \][/tex]
According to the exponent multiplication property:
[tex]\[ 3^6 \times 3^5 = 3^{6+5} = 3^{11} \][/tex]
2. Now carry out the division with the exponent of the base 3:
[tex]\[ \frac{3^{11}}{3^7} \][/tex]
According to the exponent division property:
[tex]\[ \frac{3^{11}}{3^7} = 3^{11-7} = 3^4 \][/tex]
3. Express the result in the required form [tex]\( n:1 \)[/tex]:
[tex]\[ 3^4 = 81 \][/tex]
Thus, in the required form [tex]\( n:1 \)[/tex]:
[tex]\[ 81:1 \][/tex]
So, [tex]\( n = 81 \)[/tex], the integer value we need.
To do this, we will use the properties of exponents. Specifically, we will use the property that states [tex]\( a^m \times a^n = a^{m+n} \)[/tex] and the property that [tex]\( \frac{a^m}{a^n} = a^{m-n} \)[/tex].
1. Combine the product of the exponents:
[tex]\[ 3^6 \times 3^5 \][/tex]
According to the exponent multiplication property:
[tex]\[ 3^6 \times 3^5 = 3^{6+5} = 3^{11} \][/tex]
2. Now carry out the division with the exponent of the base 3:
[tex]\[ \frac{3^{11}}{3^7} \][/tex]
According to the exponent division property:
[tex]\[ \frac{3^{11}}{3^7} = 3^{11-7} = 3^4 \][/tex]
3. Express the result in the required form [tex]\( n:1 \)[/tex]:
[tex]\[ 3^4 = 81 \][/tex]
Thus, in the required form [tex]\( n:1 \)[/tex]:
[tex]\[ 81:1 \][/tex]
So, [tex]\( n = 81 \)[/tex], the integer value we need.
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.