exponent law question:
Simplify the following exponents.
1. (16)(2^(x+2))
2. ((ab)^(2x+y))/(a^(x)b^(y))
(16)(2^(x+2))
= (2^4) (2^(x+2) )
= 2^(x+6)
((ab)^(2x+y))/(a^(x)b^(y))
= a^(2x+y) b^(2x+y) / ( (a^x)(b^y) )
= a^(x+y) b^(2x)
Wouldn't there be a 4 attached to the x for the first one?
no, you add the exponents and
4 + x+2 = x+6
Hm ok. If I had (x^(a-b))^a+b
..would that be multiplication or adding of the a's and b's
To simplify the given exponents, we can apply the exponent laws. Here's how you can simplify each expression:
1. (16)(2^(x+2))
To simplify this expression, we can use the rule that states (a^m)(a^n) = a^(m+n). Applying this rule, we can simplify the expression as follows:
(16)(2^(x+2)) = 16 * 2^(x+2)
Now, since 16 is equivalent to 2^4, we can rewrite the expression as:
16 * 2^(x+2) = (2^4) * 2^(x+2)
Next, we can apply the law (a^m)(a^n) = a^(m+n) once again:
(2^4) * 2^(x+2) = 2^(4 + (x+2))
Simplifying further:
2^(4 + (x+2)) = 2^(x+6)
So, the simplified expression is 2^(x+6).
2. ((ab)^(2x+y))/(a^(x)b^(y))
To simplify this expression, we can use the rule that states (a^m)/(a^n) = a^(m-n). Applying this rule, we can simplify the expression as follows:
((ab)^(2x+y))/(a^(x)b^(y)) = (a^(2x+y)b^(2x+y))/(a^(x)b^(y))
Next, we can use the law (a^m)/(a^n) = a^(m-n) to simplify further:
(a^(2x+y)b^(2x+y))/(a^(x)b^(y)) = a^(2x+y-x)/b^(y-y) = a^(x+y)/b^0
Since any non-zero number divided by 0 is undefined, b^0 is equal to 1. Therefore, the expression becomes:
a^(x+y)/1 = a^(x+y)
So, the simplified expression is a^(x+y).