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THIS IS FOR 19 POINTS!!!

Simplify. Express using exponents

  1. 5 with an exponent of 2 multiplied by 5 with an exponent of 5
  2. e with an exponent of 2 multiplied by e with an exponent of 7
  3. 2a with an exponent of 5 multiplied by 6a
  4. 4x with an exponent of 2 multiplied by -5x with an exponent of 6
  5. 7 with an exponent of 9 divided by 7 with an exponent of 3
  6. v with an exponent of 14 divided by v with an exponent of 6
  7. 15w with an exponent of 7 divided by 5w with an exponent of 2
  8. 10m with an exponent of 8 divided by 2m
  9. 2 with an exponent of 5 multiplied by 3 with an exponent of 7 multiplied by 4 with an exponent of 3 divided by 2 with an exponent of 1 multiplied by 3 with an exponent of 5 multiplied by 4
  10. 4 with an exponent of 15 multiplied by -5 with an exponent of 6 divided by 4 with an exponent of 12 multiplied by -5 with an exponent of 4
  11. 6 with an exponent of 7 multiplied by 7 with an exponent of 6 multiplied by 8 with an exponent of 5 divided by 6 with an exponent of 5 multiplied by 7 with an exponent of 5 multiplied by 8 with an exponent of 4
  12. -3 with an exponent of 6 multiplied by 10 with an exponent of 5 divided by -3 with an exponent of 4 multiplied by 10 with an exponent of 3

Verified Answer :

AL2006

1).  To multiply with like bases, add the exponents ===>  5² x 5⁵ = 5⁷

2).  Same rule.  e² x e⁷ = e⁹

3).  Same rule, but make sure to start with like bases.

2a⁵ x 6a = (2 x 6) (a⁵ x a¹) = 12 a⁶

4).  Same rule, but make sure to start with like bases.

4x² (-5)x⁶ = (4) (-5) (x² x⁶) = -20x⁸

5).  To divide with like bases, subtract the denominator (divisor) exponent
from the numerator (dividend) exponent. ===> 7⁹ / 7³ = 7⁶

6).  Same rule.    v¹⁴ / v⁶ = v⁸

7).  Same rule, but make sure to start with like bases.

15w⁷ / 5w² = (15/5) (w⁷/w²) = 3 w⁵

8).  Same rule, but make sure to start with like bases.

10 m⁸ / 2m = (10/2) (m⁸ / m¹) = 5m⁷

9).  Same rules.  Add exponents to multiply, subtract them to divide.

( 2⁵ x 3⁷ x 4³ ) / (2¹ x 3⁵ x 4) = (2⁵ / 2¹) x (3⁷ / 3⁵) x (4³ / 4¹) = 2⁴ x 3² x 4²

10).  (4¹⁵) x (-5)⁶ / (4¹² x (-5)⁴ ) = (4¹⁵/4¹²) x [ (-5)⁶/(-5)⁴ ] = 4³ x (-5)² = 4³ x 5²

11).  (6⁷ x 7⁶ x 8⁵) / (6⁵ x 7⁵ x 8⁴) = (6⁷ / 6⁵) x (7⁶ / 7⁵) x (8⁵ / 8⁴)
       You can finish it from here, you Crazy Unicorn you.

12).  [ (-3)⁶ x 10⁵ ] / [ (-3)⁴ x 10³ ]   =  [ (-3)⁶ / (-3)⁴ ] x (10⁵/10³)  
        The last step is yours.  Take it !

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