Question

Select an equivalent exponent expression for 10 to the power of 14 over 10 to the power of two squared equals 10¹⁴/10²

10²⁸
10⁷
10¹⁶
10¹²

Answer 1

The equivalent exponent expression for 10 to the power of 14 over 10 to the power of two squared is 10 to the power of 10, since when bases are the same, their exponents are subtracted in division.

Step-by-step explanation:

To find an equivalent exponent expression for 10 to the power of 14 over 10 to the power of two squared, we need to apply the rules of exponents for division. The expression 10¹⁴ divided by 10²² or 10 to the power of 2 squared simplifies to 10¹⁴ divided by 10⁴ because 10 squared (10²) is 100, and 100 to the power of 2 (100²) is 10,000 or 10⁴. According to the laws of exponents, when dividing like bases, we subtract the exponents, so 10¹⁴ divided by 10⁴ yields 10¹⁴-4 or 10±⁰. Therefore, the equivalent exponent expression is 10 to the power of 10, or 10±⁰.