plify each expression below using the properties of integer exponents. Assume $$ m= $$ ify by numerical substitution. $$ \begin{array}{ll}k^{3} * k^{5} & ext { b. } m^{5} * m^{-2}\end{array} $$

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plify each expression below using the properties of integer exponents. Assume $$ m= $$ ify by numerical substitution. $$ \begin{array}{ll}k^{3} * k^{5} & 	ext { b. } m^{5} * m^{-2}\end{array} $$

UpStudy AI · Accepted Answer

1. To simplify $$ k^{3} \cdot k^{5} $$, we use the property of exponents that states  
   $$
   a^{m} \cdot a^{n} = a^{m+n}.
   $$
   Thus,  
   $$
   k^{3} \cdot k^{5} = k^{3+5} = k^{8}.
   $$

For numerical substitution, if we let $$ k=2 $$:
   $$
   k^{3} \cdot k^{5} = 2^3 \cdot 2^5 = 8 \cdot 32 = 256,
   $$
   and also,
   $$
   k^8 = 2^8 = 256.
   $$
   The results match.

2. To simplify $$ m^{5} \cdot m^{-2} $$, we again use the property of exponents:
   $$
   m^{5} \cdot m^{-2} = m^{5+(-2)} = m^{3}.
   $$

For numerical substitution, if we let $$ m=3 $$:
   $$
   m^{5} \cdot m^{-2} = 3^5 \cdot 3^{-2} = 243 \cdot \frac{1}{9} = 27,
   $$
   and also,
   $$
   m^3 = 3^3 = 27.
   $$
   The results are consistent.
$$ k^{3} \cdot k^{5} = k^{8} $$ and $$ m^{5} \cdot m^{-2} = m^{3} $$.

plify each expression below using the properties of integer exponents. Assume \( m= \) ify by numerical substitution. \( \begin{array}{ll}k^{3} * k^{5} & \text { b. } m^{5} * m^{-2}\end{array} \)

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