Question

Which expression is equivalent to the one in the picture?

Answer 1

d.

Explanation:

To convert a root to a fraction in the exponent, remember this rule:

`\sqrt[n]{a^(m)}=a^{(m)/(n)}`

The index becomes the denominator in the fraction. (The index is the little number in front of the root, "n".) The original exponent remains in the numerator.

In this question, the index is 4.

The index is applied to every base in the equation under the root. The bases are 16, 'x' and 'y'.

`\sqrt[4]{16x^(15)y^(17)} = (\sqrt[4]{16})(\sqrt[4]{x^(15)})(\sqrt[4]{y^(17)}) = (2)(x^{(15)/(4)}})(y^{(17)/(4)}) = 2x^{(15)/(4)}}y^{(17)/(4)}`

To find the quad root of 16, input this into your calculator. Since 2⁴ = 16,
`\sqrt[4]{16}` = 2.

For the "x" and "y" bases, use the rule for converting roots to exponent fractions. The index, 4, becomes the denominator in each fraction.

`2x^{(15)/(4)}y^{(17)/(4)}`