Answer:
Step-by-step explanation:
[tex]a^{-m}=\frac{1}{a^{m}}\\\\\frac{1}{a^{-m}}=a^{m}\\\\\\a^{m}*a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
[tex](a^{m})^{n} = a^{m*n}[/tex]
In exponent multiplication, if two numbers have same base, just add the exponents
In exponent division, if two numbers have same base, just subtract the exponents
Prime factorize 4 = 2*2 = 2²
4⁻¹ *(2³÷ 4⁻² )= (2²)⁻¹ * ( 2³÷ (2²)⁻²
= (2⁻²)* (2³ ÷2⁻⁴)
[tex]= 2^{-2} * (2^{3-[-4]})\\\\= 2^{-2} * (2^{3+4})\\\\= 2^{-2} * 2^{7}\\\\= 2^{-2+7}\\\\= 2^{5}\\\\= 2 * 2 * 2 * 2 * 2\\\\= 32[/tex]
