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Evaluate the left hand side to find the value of
a in the equation in simplest form.

(x^(4))/(x^((1)/(6)))=x^(a)
Answer:

Evaluate the left hand side to find the value of $a$ in the equation in simplest form. $\newline$ $\frac{x^{4}}{x^{\frac{1}{6}}}=x^{a}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

Q. Evaluate the left hand side to find the value of

a

in the equation in simplest form.

\newline

\frac{x^{4}}{x^{\frac{1}{6}}}=x^{a}

\newline

Answer:

Simplify using properties of exponents: Simplify the left-hand side of the equation using the properties of exponents. When dividing powers with the same base, subtract the exponents. $\frac{x^{4}}{x^{\frac{1}{6}}} = x^{4 - \frac{1}{6}}$
Subtract exponents: Perform the subtraction of the exponents. $\newline$ $4 - \left(\frac{1}{6}\right) = \left(\frac{24}{6}\right) - \left(\frac{1}{6}\right) = \frac{23}{6}$ $\newline$ So, $\left(x^{4}\right)/\left(x^{\left(\frac{1}{6}\right)}\right) = x^{\frac{23}{6}}$
Perform subtraction: Since the left-hand side of the equation is now simplified to $x^{\frac{23}{6}}$ , we can equate this to the right-hand side of the equation. $\newline$ $x^{\frac{23}{6}} = x^{a}$
Equating left and right sides: By the property of equality for exponential equations, if the bases are the same, then the exponents must be equal. $\newline$ Therefore, $a = \frac{23}{6}$

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