Question

Which expression is equivalent to StartFraction RootIndex 7 StartRoot x squared EndRoot Over RootIndex 5 StartRoot y cubed EndRoot? Assume y not-equals 0.
(x Superscript two-sevenths Baseline) (y Superscript negative three-fifths Baseline)
(x Superscript two-sevenths Baseline) (y Superscript five-thirds Baseline)
(x Superscript two-sevenths Baseline) (y Superscript three-fifths Baseline)
(x Superscript seven-halves Baseline) (y Superscript negative five-thirds Baseline)

Answer 1

Answer:

Option A.

Step-by-step explanation:

The given expression is

$\dfrac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}$

where, $y\neq 0$.

We need to find the expression which is equivalent to the given expression.

The given expression can be rewritten as

$\dfrac{(x^2)^{\frac{1}{7}}}{(y^3)^{\frac{1}{5}}}$      $[\because \sqrt[n]{x}=x^{\frac{1}{n}}]$

$\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}$      $[\because (a^m)^n=a^{mn}]$

$x^{\frac{2}{7}}y^{-\frac{3}{5}}$      $[\because a^{-n}=\dfrac{1}{a^n}]$

Therefore, the correct option is A.

Answer 2

Answer:

it is A on edgenuity

Step-by-step explanation: