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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.