Question

How do i solve this question?
(7/x)^-3
Please provide workings.

Answer 1

To simplify the expression (7/x)^-3, we can apply the negative exponent rule.

The negative exponent rule states that when a term with a negative exponent is in the numerator or denominator of a fraction, it can be moved to the opposite position and the sign of the exponent changed to positive.

For our expression, we have:

(7/x)^-3

To apply the negative exponent rule, we can rewrite the expression as:

1 / (7/x)^3

Next, we can simplify the expression within the parentheses by raising the fraction (7/x) to the power of 3:

1 / (7^3 / x^3)

Simplifying further, we have:

1 / (343 / x^3)

To divide by a fraction, we can multiply by its reciprocal:

1 * (x^3 / 343)

Finally, we simplify by rearranging the terms:

x^3 / 343

Therefore, the simplified form of (7/x)^-3 is x^3 / 343.

Answer 2

`\sf{(x^3)/(343)}`

Explanation:

The question is asking us to solve:

`\sf{\bigg((7)/(x)\bigg)^(-3)}`

So the entire fraction is raised to the power of -3.

To simplify further, we recall the following exponent law:

`\bf{x^(-m)=(1)/(x^m)}`

So we flop the number over, like this:

`\sf{\bigg((7)/(x)\bigg)^(-3)}`

`\sf{\bigg((x)/(7)\bigg)^3}`

If we have a fraction raised to a power, then both the numerator and the denominator is raised to that power:

`\sf{(x^3)/(7^3)}`

Simplify:

`\sf{(x^3)/(343)}`

Therefore, the answer is x³/343.