Fully simplify. (-6x^(5)y^(4))^(4) Answer:

Identify base and exponent: Identify the base and the exponent in (-6x^(5)y^(4))^(4). In (-6x^(5)y^(4))^(4), the base is (-6x^(5)y^(4)) and the exponent is 4.Apply power of a product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the base. (-6x^(5)y^(4))^4 = (-6)^4 * (x^5)^4 * (y^4)^4Calculate each part: Calculate each part separately. First, calculate (-6)^4: (-6)^4 = 6^4, since an even power of a negative number is positive. 6^4 = 6 * 6 * 6 * 6 = 1296 Next, calculate (x^5)^4: (x^5)^4 = x^(5*4) = x^20 Finally, calculate (y^4)^4: (y^4)^4 = y^(4*4) = y^16Combine results: Combine the results from Step 3. (-6x^(5)y^(4))^4 = 1296 * x^20 * y^16

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Fully simplify.

(-6x^(5)y^(4))^(4)
Answer:

Fully simplify. $\newline$ $\left(-6 x^{5} y^{4}\right)^{4}$ $\newline$ Answer:

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

\left(-6 x^{5} y^{4}\right)^{4}

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-6x^{5}y^{4})^{4}$ . $\newline$ In $(-6x^{5}y^{4})^{4}$ , the base is $(-6x^{5}y^{4})$ and the exponent is $4$ .
Apply power of a product rule: Apply the power of a product rule, which states that $(ab)^n = a^n \times b^n$ , to the base.(\(-6x^{ $5$ }y^{ $4$ })^ $4$ = ( $-6$ )^ $4$ \times (x^ $5$ )^ $4$ \times (y^ $4$ )^ $4$
Calculate each part: Calculate each part separately. $\newline$ First, calculate $(-6)^4$ : $\newline$ $(-6)^4 = 6^4$ , since an even power of a negative number is positive. $\newline$ $6^4 = 6 \times 6 \times 6 \times 6 = 1296$ $\newline$ Next, calculate $(x^5)^4$ : $\newline$ $(x^5)^4 = x^{5\times4} = x^{20}$ $\newline$ Finally, calculate $(y^4)^4$ : $\newline$ $(y^4)^4 = y^{4\times4} = y^{16}$
Combine results: Combine the results from Step $3$ . $\newline$ $(-6x^{5}y^{4})^{4} = 1296 \times x^{20} \times y^{16}$