Question

4^12^*6^15*7^21 find the cube root​

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

To Find:

• Cube root of 4^12 * 6^15 * 7^21

Solution:

$\displaystyle :\longrightarrow \sqrt[3]{4^{12} * 6^{15} * 7^{21}} \\\\:\implies \sqrt[3]{4^{3*4} * 6^{3*5} * 7^{3*7}} \\\\:\implies \sqrt[3]{4^{4*3}} * \sqrt[3]{6^{5*3}} * \sqrt[3]{7^{7*3}} \\\\:\implies 4^{\frac{4*3}{3}} * 6^{\frac{5*3}{3}} * 7^{\frac{7*3}{3}} \\\\\bf{:\implies 4^4 * 6^5 * 7^7}$

Formula Used:

• a^(mn) = a^m * a^n

Learn More:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

Hope it helps!!