how would i write out this equation into a simplified experssion using exponents.
(81a^8b^4)^1/4
You need to multiply all of the exponents by the 1/4
write 81 and 3^4 first then multiply the 4 times 1/4 =1 so you just have 3^1 which is 3.
Now, can you do a and b?
when i do this i get 3a^2sqrtb is that correct?
Yes!!
To write out the equation (81a^8b^4)^(1/4) using exponents, you can follow these steps:
Step 1: Recall the exponent rule for raising a power to a power. The rule states that when you raise an exponentiated term to another power, you multiply the exponents.
Step 2: Apply the exponent rule to the given equation. In this case, you need to multiply the exponents of a and b with the exponent 1/4.
Starting with the given equation:
(81a^8b^4)^(1/4)
Now, apply the exponent rule:
81^(1/4) * (a^8)^(1/4) * (b^4)^(1/4)
Step 3: Simplify each part separately.
- Simplify 81^(1/4):
81^(1/4) can be written as the fourth root of 81. The fourth root of 81 is 3 because 3 * 3 * 3 * 3 = 81. So, 81^(1/4) simplifies to 3.
- Simplify (a^8)^(1/4):
(a^8)^(1/4) can be simplified by multiplying the exponents: 8 * 1/4 = 2. So, (a^8)^(1/4) simplifies to a^2.
- Simplify (b^4)^(1/4):
(b^4)^(1/4) can be simplified by multiplying the exponents: 4 * 1/4 = 1. So, (b^4)^(1/4) simplifies to b^1, which is just b.
Step 4: Combine the simplified parts.
Now, substitute the simplified values back into the equation:
3 * a^2 * b^1
Step 5: Further simplify, if necessary.
You can simplify the expression further by removing the unnecessary exponents:
3ab
Therefore, the simplified expression of (81a^8b^4)^(1/4) using exponents is 3ab.