Responses
(9x*4y5*)(-2x*2y*7)
11 answers
To simplify the expression \((9x^4y^5)(-2x^2y^7)\), we follow these steps:
Multiply the coefficients: \(9\) and \(-2\) give \(-18\).
Multiply the \(x\) terms: \(x^4\) and \(x^2\) can be added together since the bases are the same: \(x^{4+2} = x^6\).
Multiply the \(y\) terms: \(y^5\) and \(y^7\) can also be added together: \(y^{5+7} = y^{12}\).
Putting it all together, we have:
\[ (9x^4y^5)(-2x^2y^7) = -18x^6y^{12} \]
Therefore, the simplified expression is:
\[ \boxed{-18x^6y^{12}} \]
Yes, let’s go through the steps of simplifying the expression \((9x^4y^5)(-2x^2y^7)\) again to ensure accuracy.
Multiplying the coefficients: \[ 9 \times -2 = -18 \]
Multiplying the \(x\) terms: \[ x^4 \times x^2 = x^{4+2} = x^6 \]
Multiplying the \(y\) terms: \[ y^5 \times y^7 = y^{5+7} = y^{12} \]
Combining all parts gives us: \[ (9x^4y^5)(-2x^2y^7) = -18x^6y^{12} \]
So, the simplified expression is indeed: \[ \boxed{-18x^6y^{12}} \]
If there's any specific part you'd like to revisit or clarify, please let me know!
To simplify the expression \( \sqrt[3]{64} + 3 \left( 2 + \sqrt{5} \right) \), we'll break it down step by step.
Calculate \( \sqrt[3]{64} \): \[ \sqrt[3]{64} = 4 \]
Evaluate \( 3(2 + \sqrt{5}) \): \[ 3(2 + \sqrt{5}) = 3 \times 2 + 3 \times \sqrt{5} = 6 + 3\sqrt{5} \]
Combine the two parts: \[ 4 + 6 + 3\sqrt{5} = 10 + 3\sqrt{5} \]
Since \( 10 + 3\sqrt{5} \) does not match any particular integer choice, we should consider if we need to evaluate it further, or if the answer must be one of the provided options numerically.
Since \( 3\sqrt{5} \) is approximately \( 6.708 \) (as \( \sqrt{5} \approx 2.236 \)), the full evaluation would be roughly: \[ 10 + 6.708 \approx 16.708 \]
Looking at the provided options:
None of the options exactly match \( 10 + 3\sqrt{5} \).
If we are required to choose the closest integer, it would seem \( 17 \) is the nearest, given that \( 10 + 3\sqrt{5} \) rounds to approximately \( 17 \).
Therefore, the most reasonable choice would be:
\[ \boxed{17} \]
To simplify the expression \( \frac{2278}{2276} \), we can apply the properties of exponents.
Recall that:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In this case, we can express the numbers in terms of their bases:
\[ \frac{227^8}{227^6} = 227^{8-6} = 227^2 \]
Thus, the simplified expression is:
\[ 227^2 \]
If desired, we can further compute \( 227^2 \):
\[ 227^2 = 227 \times 227 = 51529 \]
The final answer, expressed using positive exponents, is:
\[ \boxed{227^2} \]
And if you need the numeric value, that would be \( 51529 \).
It looks like you haven't provided a specific expression to simplify. If you could share the expression, I would be glad to help you simplify it and express your answer using positive exponents!
To express the Bohr radius of a hydrogen atom, \(0.0000000000529\), in scientific notation, we need to rewrite it in the form of \(a \times 10^n\), where \(1 \leq a < 10\) and \(n\) is an integer.
Identify \(a\): Move the decimal point in \(0.0000000000529\) to the right until we have a number between 1 and 10. This gives us: \[ 5.29 \]
Count the number of places we moved the decimal: We moved it 11 places to the right. Therefore, we will use \(10^{-11}\).
Putting it all together, we have: \[ 0.0000000000529 = 5.29 \times 10^{-11} \]
Thus, in scientific notation, the Bohr radius of a hydrogen atom is:
\[ \boxed{5.29 \times 10^{-11}} \]
