SOLUTION: Use rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers. The 5 root of 3 multiplied by the cube root of z.

Question 629380: Use rational exponents to write as a single radical expression. Assume that all variables represent positive real numbers.
The 5 root of 3 multiplied by the cube root of z.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Radicals can be multiplied only if they are the same type of roots. Here we have two types, a 5th root and a cube (3rd) root. So we cannot multiply them together as they are now.

As the problem suggest, rational (fractional) exponents can be used to convert these roots so that we can multiply them. We start by rewriting the radical expressions with fractional exponents. The exponent for 5th roots is 1/5 and the exponent for cube roots is 1/3. So we can rewrite the above as:

Keeping in mind that the denominator represents the type of root, we can match the types of these roots by finding the lowest common denominator (LCD). The LCD of 3 and 5 is 15. Rewriting our expression with exponents having denominators of 15:

Using the fact that , we can switch back to radical notation:

Since we have the same types of roots we can multiply these:

And finally we can simplify the :

RELATED QUESTIONS
a. (3cubed square root xy)^6 b. square root 3cubed square root x Use rational... (answered by stanbon)

a. (cubed square root xy)^6 b. square root cubed square root x Use rational... (answered by Alan3354)

Simplify each expression. Write answers in positive exponents. Assume all variables... (answered by mananth)

Simplify the expressions nvolving rational exponents. Assume all variables represent... (answered by stanbon)

Use the rules of exponents to simplify the expression. Write the answer with positive... (answered by Alan3354)

Use the properties of exponents to simplify the expression. Write with positive... (answered by ewatrrr)

Write the following expression in simplified radical form {{{ sqrt 50y^5z^6 }}}... (answered by Alan3354)

Use the product, quotient, and power rules of logarithms to rewrite the expression as a... (answered by jsmallt9)

Use the product, quotient, and power rules of logarithms to rewrite the expression as a... (answered by jim_thompson5910)