11 answers
To simplify the expression \( t^{400} \cdot t^{100} \) using the properties of exponents, specifically the Product Rule of Integer Exponents, we add the exponents since they have the same base:
\[ t^{400} \cdot t^{100} = t^{400 + 100} = t^{500} \]
Therefore, the simplified expression is:
\( t^{500} \)
To simplify the expression \( a^{67} b^{34} \), we can consider it in the context of rules governing exponents, but it appears you may be looking for a specific format. If we rewrite the expression in terms of a fraction or using the idea of combining terms, we can break it down.
The expression can be presented in several forms, but one helpful way might be to separate the terms:
As a fraction, it could be written as: \[ \frac{a^{67}}{b^{34}} \]
If considering common bases, we don't have common terms between \(a\) and \(b\) to merge, so we would present it as it is, or as a product: \[ a^{67} b^{34} \]
None of these forms reduce the exponents or change the expression significantly, so without additional context, it remains as written.
The best interpretation among your options would be:
If you need further simplification or have additional constraints in mind, please specify!
To simplify the expression \( a^{67} b^{34} \), we need to look for ways it can be represented or manipulated, especially in fraction form.
As It Is:
In Fraction Form:
Let's translate the given responses with the simplified expression in mind:
Among your options, the most accurate representation of the expression \( a^{67} b^{34} \) would be:
Start Fraction \( a^{67} \) over \( b^{34} \)
If you have any further questions or need additional information, feel free to ask!
No, \( a^{67} b^{34} \) is not equal to \( a^{33} \).
The expression \( a^{67} b^{34} \) remains as is or can be represented as a fraction \( \frac{a^{67}}{b^{34}} \).
Here's a breakdown of the response in relation to potential simplifications:
Therefore, if the options given to you included \( a^{33} \) as one of the suggestions, that option is incorrect in relation to \( a^{67} b^{34} \).
If you still have other forms or contexts to present, or if you are equating with some other expression, please let me know!
To simplify the expression \( \frac{2365}{2332} \) using the Quotient Rule of Integer Exponents, we need to express the numbers in terms of powers of 2 and powers of 3, as follows:
Let’s first rewrite the numbers in exponential form:
Using the Quotient Rule \( \frac{a^m}{a^n} = a^{m-n} \):
For \( 2^{3} / 2^{3} \): \[ \frac{2^3}{2^3} = 2^{3 - 3} = 2^{0} = 1 \]
For \( 3^{5} / 3^{2} \): \[ \frac{3^{5}}{3^{2}} = 3^{5 - 2} = 3^{3} \]
Now multiplying the results from 1 and 2:
\[ \frac{2365}{2332} = 1 \cdot 3^{3} = 3^{3} \]
So, \( 3^{3} = 27 \).
However, the responses you provided are in numeric and exponential forms rather than direct numbers. Since none of the responses directly match \( 3^{3} \):
However, since the number associated with exponents hasn't been clarified, if we consider \( 2397 \) as \( 2^{3} \cdot 3^{7} \), it's worth noting that there might be a misunderstanding due to different representations or notations.
If \( 2397 \) is labeled as \( 2^{3} \cdot 3^{7} \), indicate that you are looking for \( 3^{3} \), as that precisely corresponds to our computations.
Please double-check your options against \( 3^{3} \) or \( 27 \). If you meant something else, kindly elaborate, and I will assist you further.
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