Rewrite the expression in the form x^(n). (x^((2)/(3)))^((5)/(2))=◻

Apply power of a power rule: To simplify the expression (x^((2)/(3)))^((5)/(2)), we need to apply the power of a power rule, which states that (a^(m))^n = a^(m*n). We will multiply the exponents together.Multiply the exponents: Now, let's multiply the exponents (2/3) and (5/2) together. (2/3) * (5/2) = (2*5)/(3*2) = 10/6Simplify the fraction: We can simplify the fraction 10/6 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. 10/6 = (10/2)/(6/2) = 5/3Final simplified expression: Now we have the simplified exponent, so the expression becomes x^(5/3).

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

(x^((2)/(3)))^((5)/(2))=◻

Rewrite the expression in the form $x^{n}$ . $\newline$ $\left(x^{\frac{2}{3}}\right)^{\frac{5}{2}}=\square$

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Math Problems

Algebra 2

Evaluate exponential functions

Full solution

Q. Rewrite the expression in the form

x^{n}

\newline

\left(x^{\frac{2}{3}}\right)^{\frac{5}{2}}=\square

Apply power of a power rule: To simplify the expression $(x^{(\frac{2}{3})})^{(\frac{5}{2})}$ , we need to apply the power of a power rule, which states that $(a^{m})^{n} = a^{m*n}$ . We will multiply the exponents together.
Multiply the exponents: Now, let's multiply the exponents $(\frac{2}{3})$ and $(\frac{5}{2})$ together. $(\frac{2}{3}) \times (\frac{5}{2}) = (\frac{2\times5}{3\times2}) = \frac{10}{6}$
Simplify the fraction: We can simplify the fraction $\frac{10}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{10}{6} = \frac{(10/2)}{(6/2)} = \frac{5}{3}$
Final simplified expression: Now we have the simplified exponent, so the expression becomes $x^{\frac{5}{3}}$ .