Question

Find the equivalent exponential expression of 6^(-7).

a) 6^7
b) 1/6^7
c) 1/6^(-7)
d) 6^(-1/7)

Answer 1

The equivalent exponential expression of 6^(-7) is 1/6^7, which is the reciprocal of the base raised to the positive exponent.

Step-by-step explanation:

The student has asked to find the equivalent exponential expression of 6^(-7). The negative exponent indicates that the base, which is 6 in this case, should be taken as the reciprocal raised to the absolute value of the exponent. Therefore, 6^(-7) is equivalent to 1/6^7.

Here's the step-by-step explanation:

• Understand that a negative exponent means the reciprocal of the base.
• Write the exponent as a positive by taking the reciprocal of the base: 6^(-7) = 1/(6^7).
• Therefore, the equivalent expression is 1/6^7, which is option b).