Question

Which expression is equivalent to 7 to the 3 power × 7 to the −5 power

A: 72


B: 77


C: 1 over 7 to the 2nd power


D: 1 over 7 to the 7th power

Answer 1

C: 1 over 7 to the 2nd power

Explanation:

The question is:
`7^(3) * 7^(-5)`

When multiplying exponents, the base stays the same, while the power is added. In this question, the powers are 3 and -5.

`3+-5=-2`

The exponent will become:
`7^(-2)`

Since the power is negative, it is improper. The negative can be removed by moving the power down and making it a fraction over 1.

`7^(-2) \rightarrow (1)/(7^(2) )`

The answer is
`(1)/(7^(2))`, also written as "1 over 7 to the 2nd power".