Question

Exponents math help!

Answer 1

ANSWER


`\frac{ {m}^(2) {n}^( - 5) }{ {m}^( 7) {n}^( - 17) } = \frac{ {n}^(12) }{ {m}^(5) }`



EXPLANATION


The given expression is


`\frac{ {m}^(2) {n}^( - 5) }{ {m}^( 7) {n}^( - 17) }`


Recall the following law of exponents,


`\frac{ {a}^(m) }{ {a}^(n) } = {a}^(m - n)`


We apply this law to obtain:




`\frac{ {m}^(2) {n}^( - 5) }{ {m}^( 7) {n}^( - 17) } = {m}^(2 - 7) {n}^( - 5 - - 17)`


This simplifies to,


`\frac{ {m}^(2) {n}^( - 5) }{ {m}^( 7) {n}^( - 17) } = {m}^( 2- 7) {n}^( - 5 + 17)`


`\frac{ {m}^(2) {n}^( - 5) }{ {m}^( 7) {n}^( - 17) } = {m}^( - 5) {n}^( 12)`

Recall again that,



`{a}^( - m) = \frac{1}{ {a}^(m) }`

This implies that,



`\frac{ {m}^(2) {n}^( - 5) }{ {m}^( 7) {n}^( - 17) } = \frac{ {n}^(12) }{ {m}^(5) }`

The correct answer is D.

Answer 2

n¹²/m⁵

Explanation:

In indices; 1/a = a⁻¹

1/a⁻² = a²

So, with this information we can simplify the expression as shown bellow;

(m²n⁻⁵)/(m⁷n⁻¹⁷) = m²n⁻⁵m⁻⁷n¹⁷

= m²⁻⁷n⁻⁵⁺¹⁷

= m⁻⁵n¹²

= (n¹²)/(m⁵)

= n¹²/m⁵

The answer is D.