Fully simplify. (-6x^(2)y^(4))^(4) Answer:

Identify base and exponent: Identify the base and the exponent in (-6x^(2)y^(4))^(4). In (-6x^(2)y^(4))^(4), the base is -6x^(2)y^(4) and the exponent is 4.Apply power of power rule: Apply the power of a power rule, which states that (a^m)^n = a^(m*n). (-6x^(2)y^(4))^(4) = (-6)^4 * (x^(2))^4 * (y^(4))^4Calculate each part: Calculate each part separately. First, calculate (-6)^4: (-6)^4 = 6^4, because the negative sign becomes positive when raised to an even power. 6^4 = 6*6*6*6 = 1296 Next, calculate (x^(2))^4: (x^(2))^4 = x^(2*4) = x^8 Finally, calculate (y^(4))^4: (y^(4))^4 = y^(4*4) = y^16Combine results: Combine the results from Step 3. (-6x^(2)y^(4))^(4) = 1296 * x^8 * y^16

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Fully simplify.

(-6x^(2)y^(4))^(4)
Answer:

Fully simplify. $\newline$ $\left(-6 x^{2} y^{4}\right)^{4}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(-6 x^{2} y^{4}\right)^{4}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-6x^{2}y^{4})^{4}$ . $\newline$ In $(-6x^{2}y^{4})^{4}$ , the base is $-6x^{2}y^{4}$ and the exponent is $4$ .
Apply power of power rule: Apply the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $(-6x^{2}y^{4})^{4} = (-6)^4 * (x^{2})^4 * (y^{4})^4$
Calculate each part: Calculate each part separately. $\newline$ First, calculate $(-6)^4$ : $\newline$ $(-6)^4 = 6^4$ , because the negative sign becomes positive when raised to an even power. $\newline$ $6^4 = 6\times6\times6\times6 = 1296$ $\newline$ Next, calculate $(x^{2})^4$ : $\newline$ $(x^{2})^4 = x^{2\times4} = x^8$ $\newline$ Finally, calculate $(y^{4})^4$ : $\newline$ $(y^{4})^4 = y^{4\times4} = y^{16}$
Combine results: Combine the results from Step $3$ . $\newline$ $(-6x^{2}y^{4})^{4} = 1296 \times x^{8} \times y^{16}$