Question

Solve these using a negative exponent
a)7⁻¹²x7⁵
b)3⁴/3⁶
c)10⁻¹⁰x10⁵
d)8¹²/8¹⁵

Answer 1

To solve these expressions, one must apply the laws of exponents: adding exponents when multiplying and subtracting exponents when dividing, keeping the same base. The solutions are 7⁻⁷, 3⁻², 10⁻⁵, and 8⁻³, respectively.

Step-by-step explanation:

To solve the given problems using negative exponents, we will apply the laws of exponents. Here's how we solve each one:

1. 7⁻¹² × 7⁵: Add the exponents when multiplying with the same base. So, 7⁻¹² × 7⁵ = 7⁻¹²⁰⁵ = 7⁻⁷.
2. 3⁴ / 3⁶: Subtract the exponents when dividing with the same base. Thus, 3⁴ / 3⁶ = 3² (4-6) = 3⁻².
3. 10⁻¹⁰ × 10⁵: Again, add the exponents when multiplying with the same base. Therefore, 10⁻¹⁰ × 10⁵ = 10⁻¹⁰⁵ = 10⁻⁵.
4. 8¹² / 8¹µ: Subtract the exponents when dividing with the same base. Consequently, 8¹² / 8¹µ = 8² (12-15) = 8⁻³.

Each result expresses a number with a negative exponent, which can also be written as the reciprocal of that number raised to the positive exponent (e.g., a⁻⁻ = 1/a⁻).