Question
write an equivalent expression for \frac{1}{y-\frac{1}{4}} using positive exponents
Answers
Answer
make it less giberish
Answer
what is \(\frac{1}{{y - \frac{1}{4}}}\)
Answered by
GPT 3.5
To express the fraction \(\frac{1}{{y - \frac{1}{4}}}\) using positive exponents, we can start by rewriting the denominator.
Recall that \(\frac{1}{x}\) is equivalent to \(x^{-1}\).
Therefore, we have:
\[\frac{1}{{y - \frac{1}{4}}} = \frac{1}{{y - \left(\frac{1}{4}\right)}} = \frac{1}{{y - 4^{-1}}}\]
Now, we can rewrite \(4^{-1}\) using positive exponents.
Recall that \(a^{-n}\) is equivalent to \(\frac{1}{a^n}\).
So, \(4^{-1} = \frac{1}{4^1}\)
Thus, we can rewrite the expression as:
\[\frac{1}{{y - 4^{-1}}} = \frac{1}{{y - \frac{1}{4^1}}}\]
Let's simplify the fraction within the denominator further.
Recall that dividing by a fraction is the same as multiplying by its reciprocal.
Therefore, we can rewrite \(\frac{1}{4^1}\) as \(\frac{1}{4}\).
So, the expression can be simplified as:
\[\frac{1}{{y - \frac{1}{4^1}}} = \frac{1}{{y - \frac{1}{4}}}\]
Thus, the equivalent expression for \(\frac{1}{{y - \frac{1}{4}}}\) using positive exponents is \(\frac{1}{{y - \frac{1}{4}}}\).
Recall that \(\frac{1}{x}\) is equivalent to \(x^{-1}\).
Therefore, we have:
\[\frac{1}{{y - \frac{1}{4}}} = \frac{1}{{y - \left(\frac{1}{4}\right)}} = \frac{1}{{y - 4^{-1}}}\]
Now, we can rewrite \(4^{-1}\) using positive exponents.
Recall that \(a^{-n}\) is equivalent to \(\frac{1}{a^n}\).
So, \(4^{-1} = \frac{1}{4^1}\)
Thus, we can rewrite the expression as:
\[\frac{1}{{y - 4^{-1}}} = \frac{1}{{y - \frac{1}{4^1}}}\]
Let's simplify the fraction within the denominator further.
Recall that dividing by a fraction is the same as multiplying by its reciprocal.
Therefore, we can rewrite \(\frac{1}{4^1}\) as \(\frac{1}{4}\).
So, the expression can be simplified as:
\[\frac{1}{{y - \frac{1}{4^1}}} = \frac{1}{{y - \frac{1}{4}}}\]
Thus, the equivalent expression for \(\frac{1}{{y - \frac{1}{4}}}\) using positive exponents is \(\frac{1}{{y - \frac{1}{4}}}\).
Answered by
GPT 3.5
To express the fraction \(\frac{1}{{y - \frac{1}{4}}}\) using positive exponents, we can rewrite the denominator.
We know that \(\frac{1}{x}\) is the same as \(x^{-1}\).
So, \(\frac{1}{{y - \frac{1}{4}}}\) can be rewritten as \(\frac{1}{{y - 4^{-1}}}\).
To further simplify the expression, we note that \(4^{-1}\) is equivalent to \(\frac{1}{4^1}\).
Thus, we can rewrite the expression as \(\frac{1}{{y - \frac{1}{4^1}}}\).
Now, we simplify the fraction within the denominator by rewriting \(\frac{1}{4^1}\) as \(\frac{1}{4}\).
Finally, the expression can be simplified to \(\frac{1}{{y - \frac{1}{4}}}\).
Hence, the equivalent expression for \(\frac{1}{{y - \frac{1}{4}}}\) using positive exponents is \(\frac{1}{{y - \frac{1}{4}}}\).
We know that \(\frac{1}{x}\) is the same as \(x^{-1}\).
So, \(\frac{1}{{y - \frac{1}{4}}}\) can be rewritten as \(\frac{1}{{y - 4^{-1}}}\).
To further simplify the expression, we note that \(4^{-1}\) is equivalent to \(\frac{1}{4^1}\).
Thus, we can rewrite the expression as \(\frac{1}{{y - \frac{1}{4^1}}}\).
Now, we simplify the fraction within the denominator by rewriting \(\frac{1}{4^1}\) as \(\frac{1}{4}\).
Finally, the expression can be simplified to \(\frac{1}{{y - \frac{1}{4}}}\).
Hence, the equivalent expression for \(\frac{1}{{y - \frac{1}{4}}}\) using positive exponents is \(\frac{1}{{y - \frac{1}{4}}}\).
Answered by
GPT 3.5
To simplify the expression \(\frac{1}{{y - \frac{1}{4}}}\), we can use the concept of a common denominator.
The expression \(\frac{1}{{y - \frac{1}{4}}}\) represents the reciprocal of the quantity \(y - \frac{1}{4}\).
To find the common denominator, we need to multiply both the numerator and denominator by the same value to eliminate the fraction in the denominator.
The denominator \(y - \frac{1}{4}\) does not have any common factors, so the common denominator is simply \(y - \frac{1}{4}\).
Multiplying the numerator and denominator by the common denominator, we get:
\[\frac{1}{{y - \frac{1}{4}}} \cdot \frac{{y - \frac{1}{4}}}{{y - \frac{1}{4}}} = \frac{{1 \cdot (y - \frac{1}{4})}}{{(y - \frac{1}{4}) \cdot 1}} = \frac{{y - \frac{1}{4}}}{{y - \frac{1}{4}}}\]
Since the numerator and denominator are the same, the expression simplifies to:
\[1\]
Therefore, \(\frac{1}{{y - \frac{1}{4}}} = 1\).
The expression \(\frac{1}{{y - \frac{1}{4}}}\) represents the reciprocal of the quantity \(y - \frac{1}{4}\).
To find the common denominator, we need to multiply both the numerator and denominator by the same value to eliminate the fraction in the denominator.
The denominator \(y - \frac{1}{4}\) does not have any common factors, so the common denominator is simply \(y - \frac{1}{4}\).
Multiplying the numerator and denominator by the common denominator, we get:
\[\frac{1}{{y - \frac{1}{4}}} \cdot \frac{{y - \frac{1}{4}}}{{y - \frac{1}{4}}} = \frac{{1 \cdot (y - \frac{1}{4})}}{{(y - \frac{1}{4}) \cdot 1}} = \frac{{y - \frac{1}{4}}}{{y - \frac{1}{4}}}\]
Since the numerator and denominator are the same, the expression simplifies to:
\[1\]
Therefore, \(\frac{1}{{y - \frac{1}{4}}} = 1\).
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