Fully simplify. (4x^(4)y^(3))^(5) Answer:

Identify base and exponent: Identify the base and the exponent in the expression (4x^(4)y^(3))^(5). In (4x^(4)y^(3))^(5), the base is 4x^(4)y^(3) and the exponent is 5.Apply power of product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the expression. (4x^(4)y^(3))^(5) = 4^5 * (x^(4))^5 * (y^(3))^5Calculate powers separately: Calculate the powers separately. 4^5 = 4 * 4 * 4 * 4 * 4 = 1024 (x^(4))^5 = x^(4*5) = x^(20) (y^(3))^5 = y^(3*5) = y^(15)Combine results for final expression: Combine the results from Step 3 to get the final simplified expression. (4x^(4)y^(3))^(5) = 1024 * x^(20) * y^(15)

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Fully simplify.

(4x^(4)y^(3))^(5)
Answer:

Fully simplify. $\newline$ $\left(4 x^{4} y^{3}\right)^{5}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(4 x^{4} y^{3}\right)^{5}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in the expression 4x^{4}y^{3})^{5}\. In \$4x^{4}y^{3})^{5}\, the base is \$4x^{4}y^{3} and the exponent is ${5}$ .
Apply power of product rule: Apply the power of a product rule, which states that $(ab)^n = a^n \times b^n$ , to the expression. $\newline$ (\(4x^{ $4$ }y^{ $3$ })^{ $5$ } = $4$ ^ $5$ \times (x^{ $4$ })^ $5$ \times (y^{ $3$ })^ $5$
Calculate powers separately: Calculate the powers separately. $\newline$ $4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024$ $\newline$ $(x^{4})^5 = x^{4\times5} = x^{20}$ $\newline$ $(y^{3})^5 = y^{3\times5} = y^{15}$
Combine results for final expression: Combine the results from Step $3$ to get the final simplified expression. $\newline$ $(4x^{4}y^{3})^{5} = 1024 \times x^{20} \times y^{15}$