Question

Simplify the example using exponent rules. Your answer should not include any negative exponents.

5x to the -4 power
Over
1x to the -9 power

Answer 1

`((5x)^(-4))/((1x)^(-9))` is simplified to
`(x^5)/(625)`

Explanation:

Consider the given expression "5x to the -4 power Over 1x to the -9 power".

We can write this mathematically as,

5x to the -4 power as
`(5x)^(-4)`

and 1x to the -9 power as
`(1x)^(-9)`

Thus, 5x to the -4 power Over 1x to the -9 power can be written as,
`((5x)^(-4))/((1x)^(-9))`

We have to simplify the above expression,

Consider,
`((5x)^(-4))/((1x)^(-9))`

This can be re-written as,

`\Rightarrow ((5x)^(-4))/((1x)^(-9))=((5x)^(-4))/(x^(-9))`

Solving further,

`\Rightarrow ((5x)^(-4))/(x^(-9))=(5^(-4)\cdot x^(-4))/(x^(-9))`,

using property of exponent,
`(a^x)/(a^y)=a^(x-y)`

`\Rightarrow (5^(-4)\cdot x^(-4))/(x^(-9))=5^(-4)x^(-4-(-9))`,

`\Rightarrow 5^(-4)x^(-4-(-9))=5^(-4)x^(5)`,

using property of exponent,
`a^(-x)=(1)/(a^x)`

`\Rightarrow 5^(-4)x^(5)=(x^5)/(5^4)`,

`\Rightarrow (x^5)/(5^4)=(x^5)/(625)`

Thus,
`((5x)^(-4))/((1x)^(-9))` is simplified to
`(x^5)/(625)`