What is the cube root of 27 a 12 ?

Question

What is the cube root of       27          a      12      ?

kuskdtq · Accepted Answer

Assign the term we are looking for the number n. We can then express this issue as follows:

n = \sqrt[3]{27 a^{12}}

And, because

\sqrt[n]{x} = x^{\frac{1}{n}}

we can then rewrite it as:

n = {(27 a^{12})}^{\frac{1}{3}}

Next, we can rewrite 27 as:

n = {(3^{3} a^{12})}^{\frac{1}{3}}

Now, we can use the rule of exponents to eliminate the exponent outside the parenthesis:

{(x^{a})}^{b} = x^{a \times b}

n = {(3^{3} a^{12})}^{\frac{1}{3}}

n = 3^{3 \times \frac{1}{3}} a^{12 \times \frac{1}{3}}

n = 3^{\frac{3}{3}} a^{\frac{12}{3}}

n = 3^{1} a^{4}

And by applying this exponents rule, we can finish the equation:

a^{1} = a

n = 3^{1} a^{4}

n = 3 a^{4}

Answered question