Fully simplify. (3x^(5)y^(3))^(5) Answer:

Identify base and exponent: Identify the base and the exponent in the expression (3x^(5)y^(3))^(5). In (3x^(5)y^(3))^(5), the base is (3x^(5)y^(3)) and the exponent is 5.Apply power of power rule: Apply the power of a power rule, which states that (a^m)^n = a^(m*n) for any base a and exponents m and n. (3x^(5)y^(3))^(5) = 3^(5) * (x^(5))^(5) * (y^(3))^(5)Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. 3^(5) * (x^(5*5)) * (y^(3*5)) = 3^(5) * x^(25) * y^(15)Calculate value of 3: Calculate the value of 3 raised to the power of 5. 3^(5) = 3 * 3 * 3 * 3 * 3 = 243Write final simplified expression: Write the final simplified expression. 243 * x^(25) * y^(15)

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Fully simplify.

(3x^(5)y^(3))^(5)
Answer:

Fully simplify. $\newline$ $\left(3 x^{5} y^{3}\right)^{5}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(3 x^{5} y^{3}\right)^{5}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in the expression $(3x^{5}y^{3})^{5}$ . In $(3x^{5}y^{3})^{5}$ , the base is $(3x^{5}y^{3})$ and the exponent is $5$ .
Apply power of power rule: Apply the power of a power rule, which states that $a^m)^n = a^{m*n}\ for any base \$a$ and exponents $m$ and $n$ . $(3x^{5}y^{3})^{5} = 3^{5} * (x^{5})^{5} * (y^{3})^{5}$
Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. $\newline$ $3^{5} \times (x^{5\times5}) \times (y^{3\times5})$ $\newline$ = $3^{5} \times x^{25} \times y^{15}$
Calculate value of $3$ : Calculate the value of $3$ raised to the power of $5$ . $\newline$ $3^{5} = 3 \times 3 \times 3 \times 3 \times 3$ $\newline$ $= 243$
Write final simplified expression: Write the final simplified expression. $243 \times x^{25} \times y^{15}$