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

Identify base and exponent: Identify the base and the exponent in (-6x^(5)y)^(4). In (-6x^(5)y)^(4), the base is (-6x^(5)y) and the exponent is 4.Apply power of product rule: Apply the power of a product rule, which states that (ab)^n = a^n * b^n, to the base and exponent. (-6x^(5)y)^(4) = (-6)^4 * (x^(5))^4 * y^4Calculate (-6)^4: Calculate each part separately. First, calculate (-6)^4. (-6)^4 = 6^4, since the negative sign will become positive when raised to an even power. 6^4 = 6 * 6 * 6 * 6 = 1296Calculate (x^5)^4: Now, calculate (x^(5))^4. (x^(5))^4 = x^(5*4) = x^20, using the power of a power rule which states that (a^n)^m = a^(n*m).Calculate y^4: Finally, calculate y^4. y^4 = y * y * y * yCombine calculated parts: Combine all the calculated parts to get the final simplified expression. (-6x^(5)y)^(4) = 1296 * x^20 * y^4

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate rational exponents

Full solution

Q. Fully simplify.

\newline

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

\newline

Answer:

Identify base and exponent: Identify the base and the exponent in $(-6x^{5}y)^{4}$ . $\newline$ In $(-6x^{5}y)^{4}$ , the base is $(-6x^{5}y)$ and the exponent is $4$ .
Apply power of product rule: Apply the power of a product rule, which states that $(ab)^n = a^n * b^n$ , to the base and exponent. $(-6x^{5}y)^{4} = (-6)^{4} * (x^{5})^{4} * y^4$
Calculate $(-6)^4$ : Calculate each part separately. $\newline$ First, calculate $(-6)^4$ . $\newline$ $(-6)^4 = 6^4$ , since the negative sign will become positive when raised to an even power. $\newline$ $6^4 = 6 \times 6 \times 6 \times 6 = 1296$
Calculate $(x^5)^4$ : Now, calculate $(x^{(5)})^4$ . $(x^{(5)})^4 = x^{(5*4)} = x^{20}$ , using the power of a power rule which states that $(a^n)^m = a^{(n*m)}$ .
Calculate $y^4$ : Finally, calculate $y^4$ . $\newline$ $y^4 = y \times y \times y \times y$
Combine calculated parts: Combine all the calculated parts to get the final simplified expression. $\newline$ $(-6x^{5}y)^{4} = 1296 \times x^{20} \times y^{4}$