Multiplying different bases with different exponents

In summary, when simplifying an expression containing a single radical, remember to combine the bases by adding the fractional exponents, and then simplify further using the rules of exponents. In this case, the final expression is x^(11/12)*y^(7/12).
  • #1
leroyjenkens
616
49

Homework Statement


Write an expression containing a single radical and simplify.

Homework Equations


[tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]

The Attempt at a Solution


I can't add the exponents and I can't multiply the bases. I can't take anything out of the radicals to make the bases the same. I have no idea what to do.

Thanks
 
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  • #2
leroyjenkens said:

Homework Statement


Write an expression containing a single radical and simplify.

Homework Equations


[tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]

The Attempt at a Solution


I can't add the exponents and I can't multiply the bases. I can't take anything out of the radicals to make the bases the same. I have no idea what to do.

Thanks
Hint: ##\sqrt[4]{x^3} = \sqrt[12]{x^9}##
Is that enough of a hint?
 
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  • #3
Mark44 said:
Hint: ##\sqrt[4]{x^3} = \sqrt[12]{x^9}##
Is that enough of a hint?
Yes. Thank you.
 
  • #4
leroyjenkens said:

Homework Statement


Write an expression containing a single radical and simplify.

Homework Equations


[tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]

The Attempt at a Solution


I can't add the exponents and I can't multiply the bases. I can't take anything out of the radicals to make the bases the same. I have no idea what to do.

Thanks

Of course you can combine the bases (just by adding the fractions), and you can even make them the same by putting all fractions over a common denominator.
 
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Likes Nipuna Weerasekara
  • #5
See the expression as this,
(xy)^(1/4)*(x^2y)^(1/3)
then,
apply power to x and y,
as follows,
x^(1/4)*y^(1/4)*x^(2/3)*y^(1/3)
now remember the rules,
x^(1/4+2/3)*y^(1/4+1/3)
now simplify this,
x^(11/12)*y^(7/12)
now you might get what to do next...
 

1. What is the basic concept behind multiplying different bases with different exponents?

The basic concept is that when multiplying numbers with different bases, you can rewrite the numbers using the same base and then add the exponents. For example, 23 * 42 can be rewritten as (23 * 22) * (22 * 22) = 25 * 24 = 29.

2. How do you multiply two numbers with the same base but different exponents?

You can simply add the exponents when multiplying two numbers with the same base. For example, 23 * 22 = 23+2 = 25.

3. Can you multiply numbers with negative exponents?

Yes, you can multiply numbers with negative exponents. When multiplying numbers with the same base and negative exponents, you can treat the negative exponent as a positive exponent and follow the same steps as multiplying numbers with positive exponents. For example, 2-3 * 2-2 = 2-5 = 1/25 = 1/32.

4. Is there a special rule for multiplying numbers with different bases and the same exponent?

Yes, there is a special rule called the power rule. When multiplying numbers with different bases and the same exponent, you can keep the exponent and multiply the bases together. For example, 23 * 43 = (2*4)3 = 83 = 512.

5. Can you use the commutative property when multiplying numbers with different bases?

Yes, you can use the commutative property when multiplying numbers with different bases. This means that you can change the order of the numbers without changing the result. For example, 23 * 42 = 42 * 23 = 23+2 * 4 = 25 * 4 = 32.

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