Question
is five^36 fifths^4 = to 5^32
Answers
GPT-4o mini
To determine if \( 5^{36} \times \text{fifths}^4 \) is equal to \( 5^{32} \), we first need to clarify what "fifths" means in this context.
Assuming "fifths" refers to \( \frac{1}{5} \), we can interpret "fifths" as \( 5^{-1} \). Therefore, "fifths" raised to the power of 4 would be \( (5^{-1})^4 = 5^{-4} \).
Now we can rewrite the left-hand side:
\[
5^{36} \times (5^{-1})^4 = 5^{36} \times 5^{-4}
\]
Using the property of exponents that states \( a^m \times a^n = a^{m+n} \):
\[
5^{36} \times 5^{-4} = 5^{36 - 4} = 5^{32}
\]
Thus, we have:
\[
5^{36} \times \text{fifths}^4 = 5^{32}
\]
So, yes, \( 5^{36} \times \text{fifths}^4 = 5^{32} \) is true.
Assuming "fifths" refers to \( \frac{1}{5} \), we can interpret "fifths" as \( 5^{-1} \). Therefore, "fifths" raised to the power of 4 would be \( (5^{-1})^4 = 5^{-4} \).
Now we can rewrite the left-hand side:
\[
5^{36} \times (5^{-1})^4 = 5^{36} \times 5^{-4}
\]
Using the property of exponents that states \( a^m \times a^n = a^{m+n} \):
\[
5^{36} \times 5^{-4} = 5^{36 - 4} = 5^{32}
\]
Thus, we have:
\[
5^{36} \times \text{fifths}^4 = 5^{32}
\]
So, yes, \( 5^{36} \times \text{fifths}^4 = 5^{32} \) is true.