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

a^((2)/(5))*a^(-3)=

Rewrite the expression in the form $a^{n}$ . $\newline$ $a^{\frac{2}{5}} \cdot a^{-3}=$

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Evaluate exponential functions

Full solution

Q. Rewrite the expression in the form

a^{n}

.

\newline

a^{\frac{2}{5}} \cdot a^{-3}=

Simplify expression using exponent property: To simplify the expression $a^{(2/5)}\cdot a^{-3}$ , we need to use the property of exponents that states when you multiply powers with the same base, you add the exponents. $\newline$ So, we will add the exponents $(2/5)$ and $(-3)$ .
Find common denominator for fractions: First, we need to find a common denominator to add the fractions $(\frac{2}{5})$ and $(-3)$ . Since $(-3)$ can be written as $(-\frac{3}{1})$ , the common denominator is $5$ . We will convert $(-3)$ to a fraction with a denominator of $5$ . $\newline$ (\(-3) = (-\frac{ $3$ }{ $1$ }) \times (\frac{ $5$ }{ $5$ }) = (-\frac{ $15$ }{ $5$ })
Add exponents: Now we can add the exponents $(\frac{2}{5})$ and $(-\frac{15}{5})$ . $\frac{2}{5} + (-\frac{15}{5}) = \frac{2 - 15}{5} = -\frac{13}{5}$
Final simplified expression: The simplified expression is therefore $a^{(-13/5)}$ .

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