# Simplifying an expression involving indices

• Feb 26th 2011, 03:41 PM
AliceFisher
Simplifying an expression involving indices
I know that:

$\displaystyle (7^{x+2}(-9)^{x+2}) = (-63)^{x+2}$

My brain appears to be shutting down as to the reason why, I think the rule is:

$\displaystyle x^m y^m = xy^m$

but this one is not in the textbook. If this is right any chance someone could explain why it is right (being a bit dizzy tonight).

Alice
• Feb 26th 2011, 03:45 PM
e^(i*pi)
Quote:

Originally Posted by AliceFisher
I know that:

$\displaystyle (7^{x+2}(-9)^{x+2}) = (-63)^{x+2}$

My brain appears to be shutting down as to the reason why, I think the rule is:

$\displaystyle x^m y^m = xy^m$

but this one is not in the textbook. If this is right any chance someone could explain why it is right (being a bit dizzy tonight).

Alice

This is not a rule. The actual rule is $\displaystyle x^my^m = (xy)^m$

$\displaystyle 7^{x+2} \times -9^{x+2}$ - using the rule above (since you have the same exponent) you get $\displaystyle (7 \times -9)^{x+2} = -63^{x+2}$

Since this is the correct answer I'm guessing you copied the rule down wrong
• Feb 26th 2011, 04:42 PM
AliceFisher
Thanks e^(i*pi),

I was sure that was the right answer but I was starting to doubt myself since I could not find the rule in my head or your corrected rule in the textbook. This means my final answer is right which means I can go to sleep now.