Exponents Worksheet

Answers and Explanations

1. x • x = x²
   Rewrite x • x with exponents.
   x¹ • x¹
   
   Bases are the same. Keep the base and add the exponents.
   x¹ • x¹ = x¹⁺¹ = x²
   
   
2. x + x = 2x
    x + x is not the same as x • x. This exercise requires addition of terms, not multiplication.
   
   Add:
   x + x = 1x + 1x = 2x
   
   
3. a⁴ • b⁴= a⁴b⁴
   Because the bases are different (a and b), don't add the exponents.
   a⁴ • b⁴ = a⁴b⁴
   
   
4. a^-2 • a⁶= a⁴
   Bases are the same. Keep the base and add the exponents.
   a^-2 • a⁶ = a^-2+6 = a⁴
   
   
5. (xyz)⁵ • (xyz)¹⁵= (xyz)²⁰
   Bases are the same. Keep the base and add the exponents.
   (xyz)⁵ • (xyz)¹⁵ = (xyz)⁵⁺¹⁵ = (xyz)²⁰
   
   
6. (20e)(20e)= 400e²
   Rewrite (20e)(20e) with exponents.
   (20e¹)(20e¹)
   
   Bases are the same. Keep the base and add the exponents. (Remember to multiply 20 and 20.)
   (20e¹)(20e¹) = 20* 20 * e¹ *e¹ = 400 *e¹⁺¹ = 400e²
   
   
7. (12 + y)³⁰ • (12 + y)⁸ = (12 + y)³⁸
   Bases are the same. Keep the base and add the exponents.
   (12 + y)³⁰ • (12 + y)⁸ = (12 + y)³⁰⁺⁸ = (12 + y)³⁸