Rewrite the expression using rational exponents. $x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

A) $1x2/3\frac { 1 } { x ^ { 2 / 3 } }$
B) $x ^ { 3 }$
C) $1x2\frac { 1 } { x ^ { 2 } }$
D) $1x3\frac { 1 } { x ^ { 3 } }$
E) $x ^ { 2 }$

Question

Rewrite the expression using rational exponents.

x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }

A)

1x2/3\frac { 1 } { x ^ { 2 / 3 } }

B)

x ^ { 3 }

C)

1x2\frac { 1 } { x ^ { 2 } }

D)

1x3\frac { 1 } { x ^ { 3 } }

E)

x ^ { 2 }

Joaquin Castro · Accepted Answer

Final Answer : A, Explanation :   Using the quotient property of radicals, we can simplify the expression to: x 5 3 x 7 3 = x 5 x 7 3 = 1 x 2 3 = 1 x 2 3 = 1 x 2 / 3 \frac{\sqrt[3]{x^5}}{\sqrt[3]{x^7}}=\sqrt[3]{\frac{x^5}{x^7}}=\sqrt[3]{\frac{1}{x^2}}=\frac{1}{\sqrt[3]{x^2}}=\frac{1}{x^{2/3}} 3 x 7 ​ 3 x 5 ​ ​ = 3 x 7 x 5 ​ ​ = 3 x 2 1 ​ ​ = 3 x 2 ​ 1 ​ = x 2/3 1 ​   Therefore, the answer is choice A.

Rewrite the expression using rational exponents. $x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

A) $1x2/3\frac { 1 } { x ^ { 2 / 3 } }$
B) $x ^ { 3 }$
C) $1x2\frac { 1 } { x ^ { 2 } }$
D) $1x3\frac { 1 } { x ^ { 3 } }$
E) $x ^ { 2 }$

Definitions

Learning Objectives

Learning Objectives

Related questions

Rewrite the expression using rational exponents. x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }3x7​3x5​​ A) 1x2/3\frac { 1 } { x ^ { 2 / 3 } }x2/31​ B) x3x ^ { 3 }x3 C) 1x2\frac { 1 } { x ^ { 2 } }x21​ D) 1x3\frac { 1 } { x ^ { 3 } }x31​ E) x2x ^ { 2 }x2

Definitions

Learning Objectives

Learning Objectives

Related questions

Rewrite the expression using rational exponents. $x53x73\frac { \sqrt [ 3 ] { x ^ { 5 } } } { \sqrt [ 3 ] { x ^ { 7 } } }$

A) $1x2/3\frac { 1 } { x ^ { 2 / 3 } }$
B) $x ^ { 3 }$
C) $1x2\frac { 1 } { x ^ { 2 } }$
D) $1x3\frac { 1 } { x ^ { 3 } }$
E) $x ^ { 2 }$