IDNLearn.com provides a user-friendly platform for finding answers to your questions. Discover trustworthy solutions to your questions quickly and accurately with help from our dedicated community of experts.
Sagot :
Sure, let's simplify the given expression step-by-step:
The expression given is [tex]\((3n)^{-3}\)[/tex].
1. Understanding Negative Exponents:
A negative exponent means we take the reciprocal of the base and then apply the exponent as a positive number. So, [tex]\((a)^{-b} = \frac{1}{a^b}\)[/tex].
Thus, [tex]\((3n)^{-3} = \frac{1}{(3n)^3}\)[/tex].
2. Applying the Exponent:
Now we need to apply the exponent to the entire base:
[tex]\((3n)^3 = 3^3 \cdot n^3\)[/tex].
3. Calculating Powers:
Calculate the power of 3:
[tex]\(3^3 = 3 \times 3 \times 3 = 27\)[/tex].
Thus, [tex]\((3n)^3 = 27n^3\)[/tex].
4. Forming the Reciprocals:
Now put it all together:
[tex]\((3n)^{-3} = \frac{1}{(3n)^3} = \frac{1}{27n^3}\)[/tex].
So, the simplified form of [tex]\((3n)^{-3}\)[/tex] is:
[tex]\[ \frac{1}{27n^3} \][/tex]
This is the final answer.
The expression given is [tex]\((3n)^{-3}\)[/tex].
1. Understanding Negative Exponents:
A negative exponent means we take the reciprocal of the base and then apply the exponent as a positive number. So, [tex]\((a)^{-b} = \frac{1}{a^b}\)[/tex].
Thus, [tex]\((3n)^{-3} = \frac{1}{(3n)^3}\)[/tex].
2. Applying the Exponent:
Now we need to apply the exponent to the entire base:
[tex]\((3n)^3 = 3^3 \cdot n^3\)[/tex].
3. Calculating Powers:
Calculate the power of 3:
[tex]\(3^3 = 3 \times 3 \times 3 = 27\)[/tex].
Thus, [tex]\((3n)^3 = 27n^3\)[/tex].
4. Forming the Reciprocals:
Now put it all together:
[tex]\((3n)^{-3} = \frac{1}{(3n)^3} = \frac{1}{27n^3}\)[/tex].
So, the simplified form of [tex]\((3n)^{-3}\)[/tex] is:
[tex]\[ \frac{1}{27n^3} \][/tex]
This is the final answer.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for trusting IDNLearn.com with your questions. Visit us again for clear, concise, and accurate answers.