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

Identify base and exponent: Identify the base and the exponent in (-4x^(3)y^(3))^(3). In (-4x^(3)y^(3))^(3), the base is -4x^(3)y^(3) and the exponent is 3.Apply power of a power rule: Apply the power of a power rule, which states that (a^m)^n = a^(m*n). Here, we have to raise each factor in the base to the power of 3. (-4x^(3)y^(3))^(3) = (-4)^3 * (x^(3))^3 * (y^(3))^3Calculate (-4)^3: Calculate each part separately. First, calculate (-4)^3: (-4)^3 = -4 * -4 * -4 = -64Calculate (x^(3))^3: Now, calculate (x^(3))^3: (x^(3))^3 = x^(3*3) = x^(9)Calculate (y^(3))^3: Finally, calculate (y^(3))^3: (y^(3))^3 = y^(3*3) = y^(9)Combine calculated parts: Combine all the calculated parts. (-4x^(3)y^(3))^(3) = (-4)^3 * (x^(3))^3 * (y^(3))^3 = -64 * x^(9) * y^(9)Write final simplified expression: Write the final simplified expression. The fully simplified form is -64x^(9)y^(9).

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Fully simplify.

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

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

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Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

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

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-4x^{3}y^{3})^{3}$ . $\newline$ In $(-4x^{3}y^{3})^{3}$ , the base is $-4x^{3}y^{3}$ and the exponent is $3$ .
Apply power of a power rule: Apply the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . Here, we have to raise each factor in the base to the power of $3$ . (\(-4x^{ $3$ }y^{ $3$ })^{ $3$ } = ( $-4$ )^ $3$ \times (x^{ $3$ })^ $3$ \times (y^{ $3$ })^ $3$
Calculate $(-4)^3$ : Calculate each part separately. $\newline$ First, calculate $(-4)^3$ : $\newline$ $(-4)^3 = -4 \times -4 \times -4 = -64$
Calculate $(x^{3})^{3}$ : Now, calculate $(x^{3})^{3}$ : $(x^{3})^{3} = x^{(3\cdot3)} = x^{9}$
Calculate $(y^{3})^{3}$ : Finally, calculate $(y^{3})^{3}$ : $(y^{3})^{3} = y^{(3\times3)} = y^{9}$
Combine calculated parts: Combine all the calculated parts. $\newline$ $(-4x^{3}y^{3})^{3} = (-4)^{3} \times (x^{3})^{3} \times (y^{3})^{3} = -64 \times x^{9} \times y^{9}$
Write final simplified expression: Write the final simplified expression. $\newline$ The fully simplified form is $-64x^{9}y^{9}$ .