Question

COULD I PLEASE HAVE HELP?

Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents. (1 point)

y to the one third power all over y to the one sixth power
the square root of y to the one sixth power
the ninth root of y squared
the square root of y to the sixth power
the sixth root of y

Answer 1

\[\frac{ y^{\frac{ 1 }{ 3 }} }{ y^{\frac{ 1 }{ 6}} }\]
when you have two of the same base divided like this, you can keep the base while subtracting the exponents. in this case, it would simply be y ^ (1/3 - 1/6). from there, use the properties of fractional exponents to re-write the expression as a root.

recall:
\[x^{\frac{ b }{ a }} =\sqrt[a]{x^{b}}\]
notice how the numerator b becomes the exponent inside the radicand and the denominator a becomes the root.