Simplify. (-2x^(4)y^(5))^(3)

Apply Power of Product Rule: We need to simplify the expression (-2x^(4)y^(5))^(3). To do this, we will apply the power of a product rule, which states that (ab)^n = a^n * b^n, where a and b are any real numbers or variables, and n is a positive integer.Apply Power of Product Rule: First, we apply the power of a product rule to the entire expression. This means we will raise each factor inside the parentheses to the power of 3. (-2x^(4)y^(5))^(3) = (-2)^3 * (x^(4))^3 * (y^(5))^3Calculate Cube of -2: Next, we calculate the cube of -2, which is -8. (-2)^3 = -8Apply Power of Power Rule: Now, we raise x^4 to the power of 3. According to the power of a power rule, (x^a)^b = x^(a*b), we multiply the exponents. (x^(4))^3 = x^(4*3) = x^(12)Apply Power of Power Rule: Similarly, we raise y^5 to the power of 3. (y^(5))^3 = y^(5*3) = y^(15)Combine Parts: Finally, we combine all the parts to get the simplified expression. (-2x^(4)y^(5))^(3) = -8 * x^(12) * y^(15)

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Simplify. $\newline$ $\left(-2 x^{4} y^{5}\right)^{3}$

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Math Problems

Algebra 1

Evaluate integers raised to rational exponents

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Q. Simplify.

\newline

\left(-2 x^{4} y^{5}\right)^{3}

Apply Power of Product Rule: We need to simplify the expression $(-2x^{4}y^{5})^{3}$ . To do this, we will apply the power of a product rule, which states that $(ab)^{n} = a^{n} * b^{n}$ , where $a$ and $b$ are any real numbers or variables, and $n$ is a positive integer.
Apply Power of Product Rule: First, we apply the power of a product rule to the entire expression. This means we will raise each factor inside the parentheses to the power of $3$ . $(-2x^{4}y^{5})^{3} = (-2)^{3} \times (x^{4})^{3} \times (y^{5})^{3}$
Calculate Cube of $-2$ : Next, we calculate the cube of $-2$ , which is $-8$ . $\newline$ $(-2)^3 = -8$
Apply Power of Power Rule: Now, we raise $x^4$ to the power of $3$ . According to the power of a power rule, $(x^a)^b = x^{a*b}$ , we multiply the exponents. $\newline$ $(x^{4})^3 = x^{4*3} = x^{12}$
Apply Power of Power Rule: Similarly, we raise $y^5$ to the power of $3$ . $\newline$ $(y^{5})^3 = y^{5*3} = y^{15}$
Combine Parts: Finally, we combine all the parts to get the simplified expression. $\newline$ $(-2x^{4}y^{5})^{3} = -8 \times x^{12} \times y^{15}$