# Law of Exponent - 3

by Sharina
(Philippines)

(-2x5) raise to the poer of 2/(-4x4)raise of the poer of 3=

### Comments for Law of Exponent - 3

 Oct 14, 2011 Exponents - Powers of Powers by: Staff Question: by Sharina (Philippines) (-2x5) raise to the poer of 2/(-4x4)raise of the poer of 3= Answer: (-2x⁵)² / (-4x⁴)³ When you encounter Powers of Powers [ (-2x⁵)² or (-4x⁴)³ ], multiply the exponents = [(-1)¹ * (2)¹ * (x)⁵]² / [(-1)¹ * (4)¹ * (x)⁴]³ Multiply the exponents. = [(-1)⁽¹*²⁾ * (2)⁽¹*²⁾ * (x)⁽⁵*²⁾] / [(-1)⁽¹* ³⁾ * (4)⁽¹* ³⁾ * (x)⁽⁴* ³⁾] = [(-1)⁽²⁾ * (2)⁽²⁾ * (x)⁽¹⁰⁾] / [(-1)⁽³⁾ * (4)⁽³⁾ * (x)⁽¹²⁾] = [(1) * (4) * (x¹⁰)] / [(-1) * (64) * (x¹²)] = [(1) * (4) * (x¹⁰)] / [(-1) * (64) * (x¹²)] = [(-1) * (4) * (x¹⁰)] / [(1) * (64) * (x¹²)] = (-1) * [(4) * (x¹⁰)] / [(64) * (x¹²)] = (-1) * [(2²) * (x¹⁰)] / [(2⁶) * (x¹²)] Subtract the exponents = (-1) / [(2⁽⁶⁻²⁾) * (x⁽¹²⁻¹⁰⁾)] = (-1) / [(2⁽⁴⁾) * (x⁽²⁾)] = (-1) / [(16) * (x²)] = (-1) / (16x²) = -1 / 16x² Another way: To understand the process in a little more detail, begin by considering the numerator and denominator separately. Numerator: (-2x⁵)² (-2x⁵) is repeated 2 times = (-2x⁵) * (-2x⁵) = (-2) * (x⁵) * (-2) * (x⁵) = (-2) * (-2) * (x⁵) * (x⁵) = [(-2) * (-2)] * [(x⁵) * (x⁵)] = [(-2) * (-2)] * [(x * x * x * x * x) * (x * x * x * x * x)] = (4) * [(x * x * x * x * x) * (x * x * x * x * x)] = (4) * (x * x * x * x * x * x * x * x * x * x) x is repeated 10 times = (4) * (x¹⁰) = 4 * x¹⁰ = 4x¹⁰ Denominator: (-4x⁴)³ (-4x⁴) is repeated 3 times = (-4x⁴)* (-4x⁴)* (-4x⁴) = (-4) * (x⁴) * (-4) * (x⁴) * (-4) * (x⁴) = (-4) * (-4) * (-4) * (x⁴) * (x⁴) * (x⁴) = [(-4) * (-4) * (-4)] * [(x⁴) * (x⁴) * (x⁴)] = [(-4) * (-4) * (-4)] * [(x * x * x * x) * (x * x * x * x) * (x * x * x * x)] = (-64) * [(x * x * x * x) * (x * x * x * x) * (x * x * x * x)] = (-64) * (x * x * x * x * x * x * x * x * x * x * x * x) x is repeated 12 times = (-64) * (x¹²) = -64 * x¹² = -64x¹² The original fraction can be rewritten: (-2x⁵)² / (-4x⁴)³ = 4x¹⁰/ (-64x¹²) Factor both the numerator and denominator. The common factors can be canceled: = 4x¹⁰/ (-64x¹²) = [(2 * 2) * (x * x * x * x * x * x * x * x * x * x)] / [(-1) * (2 * 2 * 2 * 2 * 2 * 2) * (x * x * x * x * x * x * x * x * x * x * x * x)] Factors which appear in the numerator AND denominator can be canceled: = {1 / [(-1) * (2 * 2 * 2 * 2) * (x * x)]} * (2 / 2) * (2 / 2) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) * (x / x) = {1 / [(-1) * (2 * 2 * 2 * 2) * (x * x)]} * (1) * (1) * (1) * (1) * (1) * (1) * (1) * (1) * (1) * (1) * (1) * (1) = {1 / [(-1) * (2 * 2 * 2 * 2) * (x * x)]} = 1 / [(-1) * (2 * 2 * 2 * 2) * (x * x)] = 1 / [(-16) * (x * x)] = 1 / [(-16) * (x²)] = -1 / [(16) * (x²)] = -1 / (16x²) = -1 / 16x² The final answer is: -1 / 16x² Thanks for writing. Staff www.solving-math-problems.com