Please Simplify:
(root5 a^7/2)^4 a^3/a^8
So confused, I tried figuring this out but need some help tracing the steps. I would appreciate some feedback! Thanks!
I have assumed that the fraction 7/2 is enclosed in parentheses, as follows:
(sqrt(5)*a(7/2))4 a3/a8
Since the bases of the exponents are "a" or 5, you only have to apply the following rules of exponents to get your answer of 25a9.
1. sqrt(5) = 51/2
2. distributive law:
(ab)x = ax bx
3. addition of exponents of same base
ax ay = ax+y
4. multiplication of exponents
(ax )y = axy
So:
(sqrt(5)*a(7/2))4 a3/a8
=(sqrt(5)4*(a(7/2))4) a3-8
=25 a14 a-5
=25 a9
WOW Thanks for the reply, but I still do not get how we get 25a^9. Can you please further explain. Thanks!
I get 25a^9/16? How can this be? Please help, still confused, thanks!
If you show your steps, it may help me spot where it has gone wrong.
...
=(sqrt(5)4*(a(7/2))4) a3-8
=5(1/2)*4*a(7/2)*4*a3-8
=25 a14 a-5
=25 a9
the denominator 2 in the fraction (7/2) is an exponent and not a simple number. This is probably from where you got the 16.
To simplify the given expression, let's break it down step-by-step:
Step 1: Simplify the expression inside the parentheses.
The expression inside the parentheses is (root5 a^7/2)^4.
To simplify this, we can apply the exponent rule that states when we raise a power to another power, we multiply the exponents.
So, (root5 a^7/2)^4 simplifies to (root5)^4 * (a^7/2)^4.
Step 2: Simplify the root (root5)^4.
When a number or expression is inside a root and raised to a power, we can simplify it by raising the number or expression inside the root to the same power.
In this case, (root5)^4 simplifies to 5^(4/2), which equals 5^2.
Step 3: Simplify the expression with the variable a.
(a^7/2)^4 simplifies to (a^(7/2 * 4)), which is equal to a^7 * 4.
Step 4: Simplify the expression outside the parentheses.
Now, we have 5^2 * a^7 * 4 * a^3 / a^8.
Step 5: Simplify the expression with the variable a.
In this step, we use the exponent rule that states when dividing two powers with the same base, we subtract the exponents.
Therefore, we have 5^2 * a^(7+3) / a^8.
5^2 simplifies to 25.
So, the final expression is 25 * a^10 / a^8.
Step 6: Simplify the expression with the variable a.
To simplify this expression, we use the exponent rule that states when dividing two powers with the same base, we subtract the exponents.
So, a^(10-8) simplifies to a^2.
Final Result:
25 * a^2
Therefore, the simplified expression is 25a^2.