Question

write the expression in exponential form (3 sqrt a)^2

Answer 1

Question says to write the given expression $(3 \sqrt{a})^2$ in exponential form.

we can start by distributing outer exponent 2 using formula

$(x*y)^n=x^n*y^n$

Using this formula we get:

$(3 \sqrt{a})^2 = 3^2 *( \sqrt{a})^2$

$(3 \sqrt{a})^2 = 3^2 *(a^{\frac{1}{2}})^2$

because square root is equivalent to fractional exponent 1/2.

Hence required exponent form is $3^2 *(a^{\frac{1}{2}})^2$

We can simplify this too to get:

$= 9 *(a^{\frac{1}{2}})^2$

$= 9 *(a^{\frac{1}{2}*2})$

$= 9 *(a^{1)$

=9a

Hence final simplified answer is 9a.