What is the simplest form of

Mathematics

1 answer:

steposvetlana [31]3 years ago

4 0

Answer:

The simplest form of $\sqrt[3]{27a^{3}b^{7}}$ is

3ab²(∛b)

Step-by-step explanation:

The given term is:

$\sqrt[3]{27a^{3}b^{7}}$

To convert it into its simplest form, we will apply simple mathematical rules to simplify the power of individual terms.

$\sqrt[3]{27a^{3}b^{7}}\\= \sqrt[3]{3^{3} a^{3}b^{7}}\\= \sqrt[3]{3^{3}a^{3}b^{6}b}\\= 3^{3/3} a^{3/3}b^{6/3}b^{1/3}}\\= 3ab^{2}(\sqrt[3]{b})$

While simplifying the term, we basically took the cube root of individual terms. The powers cancelled out cube root for some terms. In the end, we were left with the simplest form of the expression.

You might be interested in

Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .