Question
Simplify (74)9\left(7^{4}\right)^{9}(7
4
)
9
. Write your answer in exponential form. (Example: 525^25
2
not 252525 ).
4
)
9
. Write your answer in exponential form. (Example: 525^25
2
not 252525 ).
Answers
Answered by
GPT-4o mini
To simplify the expression \( (74)9(7^{4})^{9} \), let's break it down step-by-step:
1. **Recognize the terms**:
The term \( (74)9 \) is not clearly defined in the context of exponents without additional information, so let's assume it represents a multiplication of 74 by 9. For this response, if we only focus on the \( (7^4)^9 \), we can simplify that part first.
2. **Apply the power of a power rule**:
The power of a power rule states that \( (a^m)^n = a^{m \cdot n} \). Therefore, we can simplify \( (7^4)^9 \):
\[
(7^4)^9 = 7^{4 \cdot 9} = 7^{36}.
\]
3. **Combine terms**:
Since we assume \( (74)9 \) could also mean multiplying 74 and 9, it's unclear if we are combining them with \( 7^{36} \) directly. If the intent was to treat \( (74)9 \) as a coefficient separate from the exponential term of base 7, that would yield:
\[
(74)9 \text{ multiplied by } 7^{36}.
\]
But since it isn’t specified, we will treat the significant part we have as \( 7^{36} \).
Since we are looking for the expression in exponential form, the cleaned and simplified answer only from the exponential part is \( 7^{36} \).
Thus, the final answer is:
\[
\boxed{7^{36}}.
\]
1. **Recognize the terms**:
The term \( (74)9 \) is not clearly defined in the context of exponents without additional information, so let's assume it represents a multiplication of 74 by 9. For this response, if we only focus on the \( (7^4)^9 \), we can simplify that part first.
2. **Apply the power of a power rule**:
The power of a power rule states that \( (a^m)^n = a^{m \cdot n} \). Therefore, we can simplify \( (7^4)^9 \):
\[
(7^4)^9 = 7^{4 \cdot 9} = 7^{36}.
\]
3. **Combine terms**:
Since we assume \( (74)9 \) could also mean multiplying 74 and 9, it's unclear if we are combining them with \( 7^{36} \) directly. If the intent was to treat \( (74)9 \) as a coefficient separate from the exponential term of base 7, that would yield:
\[
(74)9 \text{ multiplied by } 7^{36}.
\]
But since it isn’t specified, we will treat the significant part we have as \( 7^{36} \).
Since we are looking for the expression in exponential form, the cleaned and simplified answer only from the exponential part is \( 7^{36} \).
Thus, the final answer is:
\[
\boxed{7^{36}}.
\]
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