Multiplying integers with fractions.
- Thread starter Hollis
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Hollis said:
(xy)1/3*(x^2y^2)1/2 means \(\displaystyle (xy)\cdot \frac{1}{3}\cdot (x^2y^2)\cdot \frac{1}{2}\).
Is that what you mean? If so, (xy)1/3*(x^2y^2)1/2=(1/3)(1/2)(xy)(x[sup:3pr4gwdq]2[/sup:3pr4gwdq]y[sup:3pr4gwdq]2[/sup:3pr4gwdq])=(1/6)x[sup:3pr4gwdq]3[/sup:3pr4gwdq]y[sup:3pr4gwdq]3[/sup:3pr4gwdq].
mmm4444bot
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Are the fractions exponents? In other words, does the expression in your exercise look like the following?
\(\displaystyle (xy)^{1/3} \cdot (x^2y^2)^{1/2}\)
mmm4444bot
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Hollis said:
That makes a big difference! (You posted something else, entirely.)
We use the caret symbol ^ (shift-6, on most keyboards) to denote exponents. If an exponent is more than a single object (eg: a whole number or single variable), then we need to enclose it in parentheses, to be clear.
Here's how we type the expression, in your exercise.
(xy)^(1/3) * (x^2 y^2)^(1/2)
In order to simplify this expression, you need to learn some Properties of Exponents.
Namely, the following properties.
(ab)^n = a^n b^n
In other words, if a factorized product (like xy, for example) is raised to a power, then each factor gets raised to the power.
(a^n)^m = a^(n*m)
In other words, if a power is raised to another power (like raising x^2 to the power 1/2, for example), then we multiply the two exponents.
a^n * a^m = a^(n + m)
In other words, if two powers with the same base are multiplied (like x^[1/3] and x^[3/3], for example), then we add the two exponents.
Does any of this look familiar? Can you apply these properties to simplify the given expression?
If you get stuck, then reply with specific questions. We can provide an example that's similar, but we like to see some effort first.
