Question

What is the misssing exponet 1/4x4^y=1/64

Answer 1

To solve the equation \(\frac{1}{4} \cdot 4^y = \frac{1}{64}\), we can start by simplifying it.

First, we can express \(\frac{1}{4}\) and \(\frac{1}{64}\) as powers of 4:
- \(\frac{1}{4} = 4^{-1}\)
- \(\frac{1}{64} = 4^{-3}\)

Now, substitute these into the equation:
\[
4^{-1} \cdot 4^y = 4^{-3}
\]

Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), we can combine the left side:
\[
4^{-1 + y} = 4^{-3}
\]

Since the bases are the same, we can set the exponents equal to each other:
\[
-1 + y = -3
\]

Now, solve for \(y\):
\[
y = -3 + 1
\]
\[
y = -2
\]

Thus, the missing exponent \(y\) is \(-2\).