1. ## Indices simplification

Use the laws of indices to simplify each of the following, giving answers with positive indices only.

SQRL{81A^6.B^2.C^-4/36A^2.B^6.C^4}

2. $\displaystyle \sqrt{\frac{81a^6 \cdot b^2 \cdot c^{-4}}{36a^2 \cdot b^6 \cdot c^4}}$

$\displaystyle \sqrt{\frac{9a^6 \cdot b^2 \cdot c^{-4}}{4a^2 \cdot b^6 \cdot c^4}}$

$\displaystyle \left(\frac{9a^6 \cdot b^2 \cdot c^{-4}}{4a^2 \cdot b^6 \cdot c^4} \right)^{1/2}$

$\displaystyle \frac{9a^3 \cdot b \cdot c^{-2}}{4a \cdot b^3 \cdot c^2}$

or $\displaystyle \frac{9}{4}a^{2} \cdot b^{-2} \cdot c^{-4}$

Rewriting in positive exponents we get: $\displaystyle \frac{9a^2}{4b^{2}c^{4}}$.

3. How would you do this one?

\sqrt[3]27X^8.Y.Z^-2/8X^2.Y^-2.Z^10

4. Originally Posted by gary223
How would you do this one?

\sqrt[3]27X^8.Y.Z^-2/8X^2.Y^-2.Z^10
New questions should go in new threads.

$\displaystyle \sqrt[3]{\frac{27x^8yz^{-2}}{8x^2y^{-2}z^{10}}}$

$\displaystyle =\sqrt[3]{\frac{27x^8y\frac{1}{z^2}}{8x^2\frac{1}{y^2}z^{10 }}}$

$\displaystyle =\sqrt[3]{\frac{27x^8yy^2}{8x^2z^{10}z^2}}$

$\displaystyle =\sqrt[3]{\frac{27x^8y^3}{8x^2z^{12}}}$

$\displaystyle =\sqrt[3]{\frac{3^3(x^3)^2x^2y^3}{2^3x^2(z^3)^4}}$

$\displaystyle =\frac{3x^2y}{2z^4}\sqrt[3]{\frac{x^2}{x^2}}$

$\displaystyle =\frac{3x^2y}{2z^4}$

-Dan