Question

I was wondering if you can help me on the math problemSolve:((3^2) * (7^4))^5=

Answer 1

The initial problem is:

$(3^2\times7^4)^5$

We can use the following property:

$(X^a\times Y^b)^c=X^{a\cdot c}\times Y^{b\cdot c}$

So, the initial problem is equivalent to:

$\begin{gathered} (3^2\times7^4)^5=3^{2\cdot5}\times7^{4\cdot5} \\ (3^2\times7^4)^5=3^{10}\times7^{20} \end{gathered}$

Then, solving 3^10 and 7^20, we get:

$\begin{gathered} 3^{10}=59049 \\ 7^{20}=7.98\times10^{16} \end{gathered}$

So, the answer is:

$(3^2\times7^4)^5=59049\times7.98\times10^{16}=4.71\times10^{21}$