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$Express the given expression as an integer or as a fraction in simplest form. log(10^(-(1)/(4))) Answer:$

Express the given expression as an integer or as a fraction in simplest form. $\newline$ $\log \left(10^{-\frac{1}{4}}\right)$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.

\newline

\log \left(10^{-\frac{1}{4}}\right)

\newline

Answer:

Understand Logarithm Properties: Understand the properties of logarithms. The logarithm of a power of $10$ can be simplified using the property $\log(a^b) = b \cdot \log(a)$ , where $a$ is the base of the logarithm and $b$ is the exponent.
Apply Logarithm Power Rule: Apply the logarithm power rule to the given expression. $\newline$ $\log(10^{-\frac{1}{4}})$ can be simplified by bringing the exponent in front of the logarithm. $\newline$ $\log(10^{-\frac{1}{4}}) = -\frac{1}{4} \cdot \log(10)$
Simplify Using Logarithm Base: Simplify the expression using the fact that $\log(10)$ is equal to $1$ . Since the base of the logarithm is $10$ and $\log(10) = 1$ , we can simplify the expression further. $-\left(\frac{1}{4}\right) \times \log(10) = -\left(\frac{1}{4}\right) \times 1$
Perform Multiplication: Perform the multiplication to find the final answer. $\newline$ $-\left(\frac{1}{4}\right) \times 1 = -\frac{1}{4}$

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