Rewrite the expression in the form a^(n). (a^(5))/(a^((5)/(2)))=◻^(--x)

Apply Quotient Rule: We have the expression (a^(5))/(a^((5)/(2))). To simplify, we use the quotient rule of exponents which states that when dividing like bases, we subtract the exponents. So, a^(5) / a^((5)/(2)) = a^(5 - (5/2)).Subtract Exponents: Now we need to perform the subtraction in the exponent: 5 - (5/2). To subtract these, we need a common denominator. The common denominator for 1 and 2 is 2. So we rewrite 5 as (10/2) to get a common denominator. (10/2) - (5/2) = (10 - 5) / 2 = 5/2.Find Common Denominator: Now we can rewrite the expression with the simplified exponent. a^(5 - (5/2)) = a^(5/2).Simplify Exponent: The expression a^(5/2) is already in the form a^(n), where n is 5/2. So, the expression (a^(5))/(a^((5)/(2))) simplifies to a^(5/2).

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Rewrite the expression in the form
a^(n).

(a^(5))/(a^((5)/(2)))=◻^(--x)

Rewrite the expression in the form $\newline$ $a^{n}$ . $\newline$ $\frac{a^{5}}{a^{\left(\frac{5}{2}\right)}}=\square^{-x}$

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Math Problems

Algebra 1

Evaluate integers raised to rational exponents

Full solution

Q. Rewrite the expression in the form

\newline

a^{n}

\newline

\frac{a^{5}}{a^{\left(\frac{5}{2}\right)}}=\square^{-x}

Apply Quotient Rule: We have the expression $\frac{a^{5}}{a^{\frac{5}{2}}}$ . To simplify, we use the quotient rule of exponents which states that when dividing like bases, we subtract the exponents. So, $a^{5} / a^{\frac{5}{2}} = a^{5 - \frac{5}{2}}$ .
Subtract Exponents: Now we need to perform the subtraction in the exponent: $5 - \left(\frac{5}{2}\right)$ . To subtract these, we need a common denominator. The common denominator for $1$ and $2$ is $2$ . So we rewrite $5$ as $\left(\frac{10}{2}\right)$ to get a common denominator. $\left(\frac{10}{2}\right) - \left(\frac{5}{2}\right) = \frac{10 - 5}{2} = \frac{5}{2}$ .
Find Common Denominator: Now we can rewrite the expression with the simplified exponent. $a^{5 - (\frac{5}{2})} = a^{\frac{5}{2}}$ .
Simplify Exponent: The expression $a^{\frac{5}{2}}$ is already in the form $a^{n}$ , where $n$ is $\frac{5}{2}$ . So, the expression $(a^{5})/(a^{\frac{5}{2}})$ simplifies to $a^{\frac{5}{2}}$ .