I really need help on this problem

If \(a = 4 \), \( b = 2\), and \(c = -5\) , then what is the value of \(\sqrt[3]{4a^4b^5} + \dfrac{a - c}{(b+c)^2}\)?

Plz help

Guest Jun 19, 2020

#4**0 **

Put in the numbers to get \( \sqrt[3]{4*4^4*2^5}+1\).

We can write the numbers inside the square root as powers of 2.

\( \sqrt[3]{2^2*2^8*2^5}+1\).

Now because they all have a common base, you can add the exponents. (To see why, take a basic example like\(2^2*2^3=2*2*2*2*2=2^5\). We are multiplying two 2's and three 2's which makes five threes.)

Adding the exponents, we get \( \sqrt[3]{2^{15}}+1\).

Simplifying, we get \(2^5+1\), which you can figure out on your own.

thelizzybeth Jun 19, 2020