$$a^2a^3=a^6$$

$$\left(a^2\right)^3=a^6$$

$$\left(a^2\right)^3=a^5$$

$$\left(a^2\right)^3=a^8$$

$$a^3+a^3=2a^3$$

$$a^3+a^3=a^6$$

$$a^3+a^3=a^9$$

$$\left(3ab\right)^2=9a^2b^2$$

$$\left(3ab\right)^2=3a^2b^2$$

$$\left(3ab\right)^2=6a^2b^2$$

$$2\left(ab\right)=2ab$$

$$2\left(ab\right)=2a2b$$

$$2\left(a+b\right)=2a+2b$$

$$2\left(a+b\right)=2a+b$$

$$2^4p^2\div2^2p^2=2^{\left(4-2\right)}p^{\left(2-2\right)}=2^2$$

$$2^4p^2\div2^2p^2=2^{\left(4-2\right)}p^{\left(2-2\right)}=2^2p$$

$$\left(a^2b^3\right)^4=a^8b^{12}$$

$$\left(a^2b^3\right)^4=a^6b^7$$

$$a^{-1}=\frac{1}{a}$$

$$a^{-1}=\frac{1}{-a}$$

$$a^{-1}=-a$$

$$\frac{1}{a^{-2}}=a^2$$

$$\frac{1}{a^{-2}}=a^{-2}$$

$$\left(\frac{a}{b}\right)^{-1}=\frac{b}{a}$$ , Final answer

$$\left(\frac{a}{b}\right)^{-1}=-\frac{b}{a}$$ , Final answer

$$\left(\frac{a}{b}\right)^{-1}=\frac{a}{b}$$

$$\left(\frac{a}{b}\right)^{-1}=\frac{1}{\left(\frac{a}{b}\right)}$$ , Final answer

$$\frac{a}{\left(\frac{b}{c}\right)^{-1}}=\frac{ab}{c}$$

$$\frac{a}{\left(\frac{b}{c}\right)^{-1}}=\frac{ac}{b}$$

$$2^2m^{\frac{1}{2}}=2m$$

$$\frac{a^x+2\ }{a^x}=1+2=3$$

$$2^x2^3-2^x2^{-1}=2^x\left(2^3-2^{-1}\right)$$

$$2^x2^3-2^x2^{-1}=2^x\left(2^32^{-1}\right)$$

$$2^x2^3-2^x2^{-1}=2^{\left(x-x\right)}2^{\left(3+1\right)}$$

$$2m^2=2^2m^2$$

$$\frac{2^{\left(x-3\right)}-2^{\left(x-1\right)}\ }{2^x}=2^{\left(x-3\right)}-2^{\left(x-1\right)}\div2^x\$$

$$\frac{2^x2^3-2^x2^2\ }{2^x}=2^x\left(2^3-2^2\right)$$

$$2^{\left(x+3\right)}=2^x2^3$$

$$2^{\left(x-3\right)}=2^x2^{-3}$$

$$2^{\left(x+3\right)}=2^x+2^3$$

$$2^{\left(x-3\right)}=2^x-2^{-3}$$

$$3\left(5^{\left(x+1\right)}\right)=3\left(5^x\cdot5\right)=15\cdot5^x$$

$$3\left(5^{\left(x+1\right)}\right)=3\left(5^x\cdot5\right)=3\left(5^x\right)\cdot3\left(5\right)$$

$$x^2=\frac{6^3}{x^3}$$

$$\ x^{\left(2-3\right)}=6^3$$

$$\left(a+b\right)^2=a^2+2ab+b^2$$

$$\left(\sqrt[]{x}+\sqrt[]{y}\right)^2=x+2\sqrt[]{xy}+y$$

$$\left(\sqrt[]{x}+\sqrt[]{y}\right)^2=x+y$$

$$\left(a+b\right)^2=a^2+b^2$$

$$\left(a-b\right)^2=a^2-2ab+b^2$$

$$\left(a-b\right)^2=a^2+b^2$$

$$\left(a-b\right)^2=a^2-b^2$$

$$\frac{1}{2^{\left(x+2\right)}}=2^{\left(-x-2\right)}$$

$$\frac{1}{2^{\left(x+2\right)}}=2^{\left(-x+2\right)}$$

$$\sqrt[]{x+y}=\sqrt[]{x}+\sqrt[]{y}$$

$$\sqrt[]{1+x^2}=1+x$$

$$\sqrt[]{x+y}=\sqrt[]{x}+\sqrt[]{y}$$

$$\frac{1}{6x^2}=6^{-1}x^{-2}$$

$$\frac{1}{6x^2}=6^{ }x^{-2}$$

$$\frac{2^x}{2^{\left(x+1\right)}}=\frac{2^{\left(x-2\right)}}{2^3}$$

Compare:
$$\frac{x}{x+1}=\frac{x-2}{3}$$

$$\frac{2^x}{2^{\left(x+1\right)}}=\frac{2^{\left(x-2\right)}}{2^3}$$

$$2^{\left(x-x-1\right)}=2^{\left(x-2-3\right)}$$

Compare:
$$x-x-1=x-2-3$$

$$\frac{2^x}{2^{\left(x+1\right)}}=\frac{2^{\left(x-2\right)}}{2^3}$$

Compare:
$$\frac{x}{x+1}=\frac{x-2}{3}$$

$$\frac{2x+2\ }{2}=x+1$$

$$\frac{2x+2\ }{2}=2x+1$$

$$\frac{2x+2\ }{2}=x+2$$

$$\frac{1}{2}=2^{-1}=-2$$