Question

Simplify using positive exponents

1. (5^3)^5
2. 7^-2/5^-2
3. -3(5+27)^0
4. 10^-2

Answer 1

Remember, when you distribute exponents, you distribute them to the existing exponent (if there is one) AND the coefficient. Here's the math:

1.
`(5^3)^5`

Distribute
`(^5)` to 5 and
`(^3)`


`(5^5)^3^(^5^)`

Multiply the terms accordingly


`25^1^5`

2.
`(7^-^2)/(5^-^2)`

Multiply the numerator and denominator by


`(7^-^2)/(5^-^2)=( (7)/(5))^-^2`

Use the Negative Exponent Rule to rearrange the expression


`((5)/(7))^2`

Square the numerator and denominator


`(5^2)/(7^2)`

Simplify


`(25)/(49)`

3.
`-3(5+27)^0 = 0`

If something is multiplied to the power of 0, than it is equal to 0

4.
`10^-^2`

For this, we will once again use the Negative Exponents Rule (find the reciprocal and change the negative exponent to its opposite)


`(1)/(10^2)`

Simplify


`(1)/(100)`

Answers:

1.
`25^1^5`

2.
`(25)/(49)`

3.
`0`

4.
`(1)/(100)`

Hope this helps!