# Question #7fed6

##### 2 Answers

You may write radicals as fractional powers.

#### Explanation:

In multiplication, you add the powers, so:

#### Explanation:

Here's an alternative approach

#root(5)(a^4) * root(3)(a^2) = a^n#

Once again, the first thing to do is rewrite your radicals as *exponents* by using

#color(blue)(root(y)(a^x) = a^(x/y))#

In your case, you have

#root(5)(a^4) = a^(4/5)" "# and#" "root(3)(a^2) = a^(2/3)#

Now focus on the exponents. Find their common denominator, which in this csae is

#4/5 * 3/3 = (12)/15" "# and#" "2/3 * 5/5 = 10/15#

Now the equation becomes

#a^(12/15) * a^(10/15) = a^n#

If you want to play aroun with the exponents a bit, you can convert back to radical form

#a^(12/15) = root(15)(a^12)" "# and#" "a^(10/15) = root(15)(a^(10))#

Now you have

#a^(12/15) * a^(10/15) = root(15)(a^12) * root(15)(a^(10)) = a^n#

This is equivalent to

#root(15)( a^12 * a^10) = a^n#

Once again,

#color(blue)(a^x * a^y = a^(x+y)#

so you get

#root(15)(a^(12 + 10)) = a^n#

#root(15)(a^(22)) = a^n#

Finally, convert back to exponent form to get

#a^(22/15) = a^n implies n = color(green)(22/15)#