How do you simplify $(\frac { 4x ^ { 6} y ^ { 7} } { 8x ^ { 3} } ) ^ { 4}$ ?

Question

1403 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-21T14:30:38

$(x^12y^28)/(16)$

1. Distribute the exponent of 4 - multiply every exponent inside the parentheses by 4.

Remember, the numbers without exponents actually have an exponent of 1.

$((4^4x^6y^7)/(8x^3))^4$

$= (4^4x^24y^28)/(8^4x^12)$

2. $8^4$ , which is 4096, can be rewritten as $4^6$ .

$= (4^4x^24y^28)/(4^6x^12)$

3. Use the exponent rules to simplify. When dividing powers with the same base, subtract the exponents.

$= 4^-2x^12y ^28$

This can be rewritten as

$= (x^12y^28)/(4^2)$

$= (x^12y^28)/(16)$

That's your final answer!

How do you simplify (\frac { 4x ^ { 6} y ^ { 7} } { 8x ^ { 3} } ) ^ { 4}(\frac { 4x ^ { 6} y ^ { 7} } { 8x ^ { 3} } ) ^ { 4}?