Question

Use the law of exponents to rewrite and simplify the expression:

(a) $8^{\left(\frac{4}{3}\right)}$

(b) $x{\left(3x^2\right)}^3$

Answer 1

Simplifying each expression using exponents rules:

Three most important laws of exponents used are as $x^a.x^b=x^{a+b}$, $\frac{x^a}{x^b}=x^{a-b}$ and ${\left(x^a\right)}^b=x^{a.b}$ so using these law, simplifying each expression as

(a) $8^{\left(\frac{4}{3}\right)}=2^{3.\left(\frac{4}{3}\right)}=2^4=16$

(b) $x{\left(3x^2\right)}^3=3^3.x^{1+6}=27x^7$

Hence, simplified form of (a) $8^{\left(\frac{4}{3}\right)}$ is $16$ and (b) $x{\left(3x^2\right)}^3$ is $27x^7$