Question

Express using a radical (picture provided)

Answer 1

Answer:

C

Step-by-step explanation:

First note that

$\dfrac{1}{3}=\dfrac{5}{15}\Rightarrow x^{\frac{1}{3}}=x^{\frac{5}{15}};\\ \\\\\dfrac{1}{5}=\dfrac{3}{15}\Rightarrow y^{\frac{1}{5}}=y^{\frac{3}{15}}$

Now use the property

$a^n\cdot b^n=(ab)^n,$

so

$x^{\frac{5}{15}}\cdot y^{\frac{3}{15}}=(x^5)^{\frac{1}{15}}\cdot (y^3)^{\frac{1}{15}}=(x^5y^3)^{\frac{1}{15}}.$

Since $a^{\frac{1}{15}}=\sqrt[15]{a},$

you have

$15(x^5y^3)^{\frac{1}{15}}=15\sqrt[15]{x^5y^3} .$