Simplifying Expressions with Integral Exponents| Algebra| ENGG10 LE1 Problem 1

Simplify the given expression. Write the answer with positive exponents.

\left(\frac{3^2}{a^3}\right)^{-2}\cdot \left(\frac{a^4}{2^2}\right)^2

SOLUTION:

\left(\frac{3^2}{a^3}\right)^{-2}\cdot \:\left(\frac{a^4}{2^2}\right)^2=\frac{\left(3^2\right)^{-2}}{\left(a^3\right)^{-2}}\cdot \frac{\left(a^4\right)^2}{\left(2^2\right)^2}

=\frac{3^{-4}}{a^{-6}}\cdot \frac{a^8}{2^4}

=\frac{\frac{1}{3^4}}{\frac{1}{a^6}}\cdot \frac{a^8}{2^4}

=\frac{a^6}{3^4}\cdot \frac{a^8}{2^4}

=\frac{a^6}{81}\cdot \frac{a^8}{16}

=\frac{a^{6+8}}{1296}

=\frac{a^{14}}{1296}