root(3)(81a^(5)b^(4))=

Apply cube root to factors: Apply the cube root to each factor in the expression root(3)(81a^(5)b^(4)). root(3)(81a^(5)b^(4)) = root(3)(81) * root(3)(a^(5)) * root(3)(b^(4))Calculate cube root of 81: Calculate the cube root of 81. root(3)(81) = root(3)(3^4) = 3^(4/3) = 3^(1+1/3) = 3 * 3^(1/3) Since 81 is a perfect cube (3^4), its cube root is simply 3.Simplify cube root of a^5: Simplify the cube root of a^(5). root(3)(a^(5)) = a^(5/3) = a^(1+2/3) = a * a^(2/3) We cannot simplify this further without knowing the value of 'a'.Simplify cube root of b^4: Simplify the cube root of b^(4). root(3)(b^(4)) = b^(4/3) = b^(1+1/3) = b * b^(1/3) We cannot simplify this further without knowing the value of 'b'.Combine simplified cube roots: Combine the simplified cube roots. root(3)(81a^(5)b^(4)) = 3 * a * b * (3^(1/3) * a^(2/3) * b^(1/3))Recognize cube root of 3a^2b: Recognize that the expression 3^(1/3) * a^(2/3) * b^(1/3) is the cube root of 3a^2b. root(3)(81a^(5)b^(4)) = 3ab * root(3)(3a^2b)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\sqrt[3]{81 a^{5} b^{4}}$ =

View step-by-step help

Home

Math Problems

Algebra 2

Roots of rational numbers

Full solution

\sqrt[3]{81 a^{5} b^{4}}

Apply cube root to factors: Apply the cube root to each factor in the expression $\sqrt[3]{81a^{5}b^{4}}$ . $\sqrt[3]{81a^{5}b^{4}} = \sqrt[3]{81} \cdot \sqrt[3]{a^{5}} \cdot \sqrt[3]{b^{4}}$
Calculate cube root of $81$ : Calculate the cube root of $81$ . $\newline$ $\sqrt[3]{81} = \sqrt[3]{3^4} = 3^{\frac{4}{3}} = 3^{1+\frac{1}{3}} = 3 \times 3^{\frac{1}{3}}$ $\newline$ Since $81$ is a perfect cube ( $3^4$ ), its cube root is simply $3$ .
Simplify cube root of $a^5$ : Simplify the cube root of $a^{5}$ . $\sqrt[3]{a^{5}} = a^{\frac{5}{3}} = a^{1+\frac{2}{3}} = a \cdot a^{\frac{2}{3}}$ We cannot simplify this further without knowing the value of ' $a$ '.
Simplify cube root of $b^4$ : Simplify the cube root of $b^{4}$ .
$\sqrt[3]{b^{4}} = b^{\frac{4}{3}} = b^{1+\frac{1}{3}} = b \cdot b^{\frac{1}{3}}$
We cannot simplify this further without knowing the value of $'b'$ .
Combine simplified cube roots: Combine the simplified cube roots. $\sqrt[3]{81a^{5}b^{4}} = 3 \cdot a \cdot b \cdot (3^{\frac{1}{3}} \cdot a^{\frac{2}{3}} \cdot b^{\frac{1}{3}})$
Recognize cube root of $3a^2b$ : Recognize that the expression $3^{(1/3)} \cdot a^{(2/3)} \cdot b^{(1/3)}$ is the cube root of $3a^2b$ .
$\sqrt[3]{81a^{5}b^{4}} = 3ab \cdot \sqrt[3]{3a^2b}$