How do you simplify (\frac { x ^ { 7} y ^ { 3} } { x } ) ^ { \frac { 1} { 3} }?

2 Answers
May 3, 2018

Here's how it's done

Explanation:

Cancel common factor x
=x^6y^3
\=(x^6y^3\)^{\frac{1}{3}}

Apply the exponent rule
=\(x^6\)^{\frac{1}{3}}\(y^3\)^{\frac{1}{3}}

Final solution
=x^2y

May 4, 2018

" "
color(blue)((\frac { x ^ { 7} y ^ { 3} } { x } ) ^ { \frac { 1} { 3} }=x^2y

Explanation:

" "
Given the expression: color(red)((\frac { x ^ { 7} y ^ { 3} } { x } ) ^ { \frac { 1} { 3} }

"Exponents formula required: "

color(blue)( a^m/a^n = a^(m-n)

color(blue)( a^m*a^n = a^(m+n)

color(blue)(( a^m)^(1/n) = a^(m/n)

color(green)("Step 1:"

Rewrite the given expression: color(brown)((\frac { x ^ { 7} y ^ { 3} } { x } ) ^ { \frac { 1} { 3} } as

[[(x^7*y^3)^(1/3)]]/[[x^(1/3)]

Rewrite as:

[(x^7)^(1/3)*(y^3)^(1/3)]/x^(1/3)

color(green)("Step 2:"

Use: color(blue)(( a^m)^(1/n) = a^(m/n)

Simplify:

(x^(7/3)*y^(3/3))/x^(1/3)

color(green)("Step 3:"

(x^(7/3)*y^1)/x^(1/3)

color(green)("Step 4:"

Use: color(blue)( a^m/a^n = a^(m-n)

[x^(7/3)-x^(1/3)]*y

x^(6/3)*y

rArr x^2*y

Hence,

color(blue)((\frac { x ^ { 7} y ^ { 3} } { x } ) ^ { \frac { 1} { 3} }=x^2y

Hope it helps.