Question 24456
<pre>(-8p^2q)(-4p^4q^5)=?
<b><font size = 4>
(-8p<sup>2</sup>q)(-4p<sup>4</sup>q<sup>5</sup>)

Put each factor in separate parentheses:

(-8)(p<sup>2</sup>)(q)(-4)(p<sup>4</sup>)(q<sup>5</sup>)

Rearrange them with numbers first, p's next, q's last

(-8)(-4)(p<sup>2</sup>)(p<sup>4</sup>)(q)(q<sup>5</sup>)

Multiply the numbers (-8)(-4) = +32

32(p<sup>2</sup>)(p<sup>4</sup>)(q)(q<sup>5</sup>)

To multiply (p<sup>2</sup>)(p<sup>4</sup>), add the exponents p<sup>2+4</sup> = p<sup>6</sup>

32p<sup>6</sup>(q)(q<sup>5</sup>)

Give the q the exponent 1

32p<sup>6</sup>(q<sup>1</sup>)(q<sup>5</sup>)

To multiply (q<sup>1</sup>)(q<sup>5</sup>), add the exponents q<sup>1+5</sup> = q<sup>6</sup>

32p<sup>6</sup>q<sup>6</sup>

Edwin
AnlytcPhil@aol.com</pre>