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

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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!