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

Identify base and exponent: Identify the base and the exponent in (4x^(4)y^(4))^(5). In (4x^(4)y^(4))^(5), the base is (4x^(4)y^(4)) 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 real number a and integers m and n. (4x^(4)y^(4))^(5) = 4^(5) * (x^(4))^5 * (y^(4))^5Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. 4^(5) * x^(4*5) * y^(4*5) = 4^(5) * x^(20) * y^(20)Calculate value of 4: Calculate the value of 4 raised to the power of 5. 4^(5) = 4 * 4 * 4 * 4 * 4 = 1024Combine results: Combine the results to express the fully simplified form. 1024 * x^(20) * y^(20)

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Fully simplify.

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

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

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

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

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(4x^{4}y^{4})^{5}$ . $\newline$ In $(4x^{4}y^{4})^{5}$ , the base is $(4x^{4}y^{4})$ 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 real number $a$ and integers $m$ and $n$ . $(4x^{4}y^{4})^{5} = 4^{5} * (x^{4})^5 * (y^{4})^5$
Multiply exponents: Multiply the exponents inside the parentheses by the exponent outside the parentheses. $\newline$ $4^{5} \times x^{4\times5} \times y^{4\times5}$ $\newline$ = $4^{5} \times x^{20} \times y^{20}$
Calculate value of $4$ : Calculate the value of $4$ raised to the power of $5$ . $\newline$ $4^{5} = 4 \times 4 \times 4 \times 4 \times 4$ $\newline$ $= 1024$
Combine results: Combine the results to express the fully simplified form. $1024 \times x^{20} \times y^{20}$