Algebra II - Exponent And Radical Laws

7 flashcards · Mathematics · by luckydog789 (harrison holbrook)

1. Exponent Multiplication

   bxby=bx+yb^{x} b^{y}=b^{x+y}bxby=bx+y

2. Exponent Grouping

   (ab)x=axbx(ab)^x=a^x b^x(ab)x=axbx

3. Exponent Division Grouping

   (ab)x=axbx(\frac{a}{b})^x=\frac{a^x}{b^x}(ba​)x=bxax​

4. Exponents of Exponents

   (bx)y=bxy(b^x)^y=b^{xy}(bx)y=bxy

5. Base Equality

   if b∉{0,1,−1},bx=by if and only if x=y\text{if } b\notin \{ 0,1,-1 \}, b^x=b^y \text{ if and only if } x=yif b∈/{0,1,−1},bx=by if and only if x=y

6. Exponent Equality

   0 \text{ and } b>0, \text{ then } a^x=b^x \text{ if and only if } a=b"> if x≠0,a>0 and b>0, then ax=bx if and only if a=b\text{if } x\neq 0, a>0 \text{ and } b>0, \text{ then } a^x=b^x \text{ if and only if } a=bif x=0,a>0 and b>0, then ax=bx if and only if a=b

7. Exponent Division

   bxby=bx−y\frac{b^x}{b^y}=b^{x-y}bybx​=bx−y