# Math Help - Simplifying exponential equations

1. ## Simplifying exponential equations

Ok, here are the two equations I can't seem to solve.

10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

and

6p^-4 * (4p^3)^-1/p^-5

The answers are x^(3/2)/200 for the first equation and 3/2p^2 for the second equation.

However, I keep coming up with -1250x^(3/2)/16 for the first equation and 1/24p^2 for the second equation. I have a test monday and I need to know how to do these problems...they're frusterating.

2. Originally Posted by some_nerdy_guy
Ok, here are the two equations I can't seem to solve.

10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

and

6p^-4 * (4p^3)^-1/p^-5

The answers are x^(3/2)/200 for the first equation and 3/2p^2 for the second equation.

However, I keep coming up with -1250x^(3/2)/16 for the first equation and 1/24p^2 for the second equation. I have a test monday and I need to know how to do these problems...they're frusterating.
$Aa^n\cdot Ba^m\cdot Ca^p = ABCa^{n+m+p}$ and any coefficients are multiplied together

$\frac{10x^{-3} \cdot (5x^{-2})^{-3}}{2^4 \cdot x^{\frac{3}{2}}}$

$(5x^{-2})^{-3} = \frac{x^6}{125}$

$\frac{10x^{-3} \cdot \frac{x^6}{125}}{2^4 \cdot x^{\frac{3}{2}}} = \frac{\frac{2x^3}{25}}{16x^{\frac{3}{2}}}$

= $\frac{x^{\frac{3}{2}}}{200}$

3. Originally Posted by some_nerdy_guy
Ok, here are the two equations I can't seem to solve.

10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

and

6p^-4 * (4p^3)^-1/p^-5

The answers are x^(3/2)/200 for the first equation and 3/2p^2 for the second equation.

However, I keep coming up with -1250x^(3/2)/16 for the first equation and 1/24p^2 for the second equation. I have a test Monday and I need to know how to do these problems...they're frustrating.

Formula:

• $\frac{x^{a}}{x^{b}} =x^{a-b}$
• $x^{a} \times x^b = x^{a+b}$
• $(x^a)^b = x^{ab}$

1) 10x^-3 * (5x^-2)^-3/2^4 * x^(3/2)

$\frac{10 x^{-3} \times (5 x^{-2})^{-3}}{2^4 \times x^{3/2}}$

$\frac{10 x^{-3} \times ( x^{6})}{2^4 \times x^{3/2}\times 125}$

$\frac{ x^{-3+6} }{16 \times x^{3/2}\times 125}$

$\frac{ x^{3} }{2000 \times x^{3/2}}$

$\frac{ x^{3-\frac{3}{2}} }{200 }$

$\frac{ x^{\frac{3}{2}} }{200 }$

---------------------------------------------------------------
2) 6p^-4 * (4p^3)^-1/p^-5
$
\frac{6 p^{-4} \times (4p^3)^{-1}}{p^{-5}}$

$\frac{6 p^{-4} \times (p^{-3})}{4 \times p^{-5}}$

$\frac{6 p^{-4-3} }{4 \times p^{-5}}$

$\frac{6 p^{-4-3-(-5)} }{4 }$

$\frac{6 p^{-2} }{4 }$

$\frac{3 }{2p^2 }$