root(4)(162a^(8)) (A) 3a^(2)root(4)(2) B) 2aroot(4)(7a^(3)) C) 3root(4)(3a^(3)) D) 3aroot(4)(7a)

Break down number into primes: Break down the number 162 into its prime factors. 162 can be factored into 2 * 81, and 81 is 3^4. So, 162 = 2 * (3^4).Write expression with prime factors: Write the expression with the prime factors inside the fourth root. root(4)(162a^(8)) = root(4)(2 * 3^4 * a^8)Simplify fourth root of each factor: Simplify the fourth root of each factor separately. The fourth root of 3^4 is 3, and the fourth root of a^8 is a^2 because (a^2)^4 = a^8. root(4)(2 * 3^4 * a^8) = 3a^2 * root(4)(2)Write final simplified expression: Write the final simplified expression. The final expression is 3a^2 * root(4)(2), which matches option (A).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\sqrt[4]{162a^{8}}$ $\newline$ (A) $3a^{2}\sqrt[4]{2}$ $\newline$ (B) $2a\sqrt[4]{7a^{3}}$ $\newline$ (C) $3\sqrt[4]{3a^{3}}$ $\newline$ (D) $3a\sqrt[4]{7a}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

\sqrt[4]{162a^{8}}

\newline

(A)

3a^{2}\sqrt[4]{2}

\newline

(B)

2a\sqrt[4]{7a^{3}}

\newline

(C)

3\sqrt[4]{3a^{3}}

\newline

(D)

3a\sqrt[4]{7a}

Break down number into primes: Break down the number $162$ into its prime factors. $\newline$ $162$ can be factored into $2 \times 81$ , and $81$ is $3^4$ . $\newline$ So, $162 = 2 \times (3^4)$ .
Write expression with prime factors: Write the expression with the prime factors inside the fourth root. $\sqrt[4]{162a^{8}} = \sqrt[4]{2 \times 3^{4} \times a^{8}}$
Simplify fourth root of each factor: Simplify the fourth root of each factor separately. $\newline$ The fourth root of $3^4$ is $3$ , and the fourth root of $a^8$ is $a^2$ because $(a^2)^4 = a^8$ . $\newline$ $\sqrt[4]{2 \cdot 3^4 \cdot a^8} = 3a^2 \cdot \sqrt[4]{2}$
Write final simplified expression: Write the final simplified expression. $\newline$ The final expression is $3a^2 \cdot \sqrt[4]{2}$ , which matches option $(A)$ .