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# Exponents Worksheet

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Simplify. Remember, any exponents in the final answer must be positive. The rules used to justify each step of the answer are in parentheses.

1) 21x2y/-15y4 = 7x2/-5y3

• Break down the exercise into pieces. Match constants with constants and variables with variables.
21/-15 * x2 * y/y4
• Whenever a variable doesn't have an exponent, automatically place a 1 in place of the exponent.
21/-15 * x2 * y1/y4
• Simplify each piece.
21/-15 = 7/-5
x2 = x2 (Reflexive Property)
y1/y4 = y-3 (Quotient of Powers)= 1/y3 (Negative Exponent)
• Put the pieces back together.
7/-5 * x2* 1/y3
7x2/-5y3

2) (5x5)3 = 125x15

• Can anything be done in the parentheses? No. Start with the Power of a Product rule.
53 * x5*3 (Power of a Product)
53 * x15 (Power of a Power)
• Simplify.
125x15

3) xy4z10 ÷ x3yz5 = y3 z5/x2

• Break down the exercise into pieces. Match constants with constants and variables with variables.
x1/x3 * y4/y1 * z10/z5
• Whenever a variable doesn't have an exponent, automatically place a 1 in place of the exponent.
x1/x3 * y4/y1 * z10/z5
• Simplify each piece.
x1/x3 = x-2 (Quotient of Powers) = 1/x2 (Negative Exponent)
y4/y1 = y3 (Quotient of Powers)
z10/z5 = z5 (Quotient of Powers)
• Put the pieces back together.
1/x2 * y3 * z5
1y3 z5/x2
y3 z5/x2

4) -42a2b5c3 ÷ 3a0b3c2 = -14a2b2c

• Break down the exercise into pieces. Match constants with constants and variables with variables.
-42/3 * a2/a0 * b5/b3 * c3/c2
• Simplify each piece.
-42/3= -14
a2/a0= a2 (Quotient of Powers)
b5/b3 = b2 (Quotient of Powers)
c3/c2= c1 (Quotient of Powers)
• Put the pieces back together.
-14a2b2c1
-14a2b2c
5) -56c-6 ÷ -7c2 = 8/c8
• Break down the exercise into pieces. Match constants with constants and variables with variables.
-56/-7 *c-6/c2
• Simplify each piece.
-56/-7 = 8
c-6/c2 = c-8 (Quotient of Powers) = 1/c8 (Negative Exponent)
• Put the pieces back together.
8 * 1/c8
8/c8

6) a5b8 ÷ a4b7 = ab

• Break down the exercise into pieces. Match constants with constants and variables with variables.
a5/a4 * b8/b7
• Simplify each piece.
a5/a4 = a1 (Quotient of Powers)
b8/b7= b1 (Quotient of Powers)
• Put the pieces back together:
a1*b1
ab
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