write the following with expression using exponents \root(7)(4y)=y^(?)
what is the numerator 1 4 7 0
what is the the demanoter 4 7 1 0
please explane and show work
To rewrite the expression \(\sqrt[7]{4y}\) using exponents, we need to remember that the exponent corresponds to the nth root. In this case, the root is 7.
So, we can rewrite \(\sqrt[7]{4y}\) as \((4y)^{\frac{1}{7}}\).
To find the exponent of y, we need to multiply the exponent of (4y) with the exponent of 4 and the exponent of y separately.
The exponent of (4y) is \(\frac{1}{7}\), the exponent of 4 is 1, and the exponent of y is also 1.
So, the exponent of y is \(\frac{1}{7} \cdot 1 \cdot 1 = \frac{1}{7}\).
Therefore, \(y^{\frac{1}{7}}\) is the answer to the expression \(\sqrt[7]{4y}\).
Now, let's calculate the numerator and denominator of the fraction \(\frac{1}{4^7}\).
The numerator is 1^7 = 1, and the denominator is 4^7 = 16384.
So, the numerator is 1 and the denominator is 16384.
To summarize:
- The expression \(\sqrt[7]{4y}\) can be written as \(y^{\frac{1}{7}}\).
- The numerator of \(\frac{1}{4^7}\) is 1.
- The denominator of \(\frac{1}{4^7}\) is 16384.