BLAST FROM THE PAST Simplify each expression. 1.) $$ w^{4} \cdot w^{6}= $$ $$ \qquad $$ 24 2.) $$ \left(8^{5}\right)^{3}= $$ $$ \qquad $$ $$ \lambda $$ 3.) $$ n^{3} \cdot n^{4}= $$ $$ \qquad $$ 0.75 4.) $$ 2 m^{6} \cdot 5 m^{3}= $$ $$ \qquad $$ $$ 10^{2} $$ 5.) $$ \frac{x^{4}}{x^{4}}= $$ $$ \qquad $$ $$ \frac{16}{6} $$ 6.) $$ \left[\left(7^{3}\right)^{2}\right]^{5}= $$ $$ \qquad $$ 3 7.) $$ \frac{4^{8}}{4^{6}}= $$ $$ \qquad $$ $$ \frac{2.5}{1.5} $$ 8.) $$ 6^{12} \cdot 6^{3}=36 $$

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1.) $$ w^{4} \cdot w^{6} $$  
  Using the law of exponents for multiplication, add the exponents:  
  $$ w^{4} \cdot w^{6} = w^{4+6} = w^{10} $$.

2.) $$ \left(8^{5}ight)^{3} $$  
  Raise a power to a power by multiplying exponents:  
  $$ \left(8^{5}ight)^{3} = 8^{5\cdot3} = 8^{15} $$.  
  (Alternatively, express $$8$$ as $$2^3$$ to get:  
  $$ 8^{15} = \left(2^{3}ight)^{15} = 2^{45} $$.)

3.) $$ n^{3} \cdot n^{4} $$  
  Add the exponents when multiplying like bases:  
  $$ n^{3} \cdot n^{4} = n^{3+4} = n^{7} $$.

4.) $$ 2 m^{6} \cdot 5 m^{3} $$  
  Group the numerical coefficients and the powers of $$m$$:  
  $$ 2 \cdot 5 = 10 $$ and $$ m^{6} \cdot m^{3} = m^{6+3} = m^{9} $$.  
  Thus, $$ 2 m^{6} \cdot 5 m^{3} = 10 m^{9} $$.

5.) $$ \frac{x^{4}}{x^{4}} $$  
  Subtract the exponents in the quotient (or note that any nonzero number divided by itself equals 1):  
  $$ \frac{x^{4}}{x^{4}} = x^{4-4} = x^{0} = 1 $$ (for $$ x
eq0 $$).

6.) $$ \left[\left(7^{3}ight)^{2}ight]^{5} $$  
  Multiply the exponents sequentially:  
  First, $$ \left(7^{3}ight)^{2} = 7^{3\cdot2} = 7^{6} $$.  
  Then, $$ \left(7^{6}ight)^{5} = 7^{6\cdot5} = 7^{30} $$.

7.) $$ \frac{4^{8}}{4^{6}} $$  
  Subtract the exponents when dividing like bases:  
  $$ \frac{4^{8}}{4^{6}} = 4^{8-6} = 4^{2} = 16 $$.

8.) $$ 6^{12} \cdot 6^{3} $$  
  Add the exponents when multiplying like bases:  
  $$ 6^{12} \cdot 6^{3} = 6^{12+3} = 6^{15} $$.
1.) $$ w^{10} $$ 2.) $$ 8^{15} $$ 3.) $$ n^{7} $$ 4.) $$ 10 m^{9} $$ 5.) $$ 1 $$ 6.) $$ 7^{30} $$ 7.) $$ 16 $$ 8.) $$ 6^{15} $$

BLAST FROM THE PAST
Simplify each expression.
1.) 24
2.)
3.) 0.75
4.)
5.)
6.) 3
7.)
8.)

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BLAST FROM THE PAST Simplify each expression. 1.) 24 2.) 3.) 0.75 4.) 5.) 6.) 3 7.) 8.)