Simplify each expression. Write answers using positive exponents.

Question

(9x⁷y^-5/3xy⁴)^-2 (3x⁴y⁹/2x^-2y^-6)³

 

Please show solution thank you!!!

Answer 1

First, simplify everything in parentheses by dividing the constants and subtracting exponents of common bases.

 

(3x⁶y^-9)^-2 ((3/2)x⁶y¹⁵)³

 

 

Next, use power raised to a power rule to get rid of outside exponents.

 

(1/9)x^-12y¹⁸  *  (27/8)x¹⁸y⁴⁵

 

 

Now we can multiply.

 

(3/8)x⁶y⁶³

Answer 2

((9x⁷y^-5)/(3xy⁴))^-2((3x⁴y⁹)/(2x^-2y^-6))³

 

Let's look at these individually first:

 

((9x⁷y^-5)/(3xy⁴))^-2

cancel the 3 into the 9

move the x in denominator to numerator as x^-1

move the y^-5 in numerator to denominator as y⁵

= ((3x⁷x^-1)/(y⁵y⁴))^-2

= (3x⁶/y⁹)^-2

= 1/[(3x⁶/y⁹)]²

= 1/(9x¹²/y¹⁸)

= y¹⁸/9x¹²

 

((3x⁴y⁹)/(2x^-2y^-6))³

move the x^-2 in denominator to numerator as x²

Move the y^-6 in denominator to numerator as y⁶

= ((3x⁴x²y⁹y⁶)/2)³

= (3x⁶y¹⁵/2)³

= 27x¹⁸y⁴⁵/8

 

(y¹⁸/9x¹²)(27x¹⁸y⁴⁵/8)

 

= (27x¹⁸y¹⁸y⁴⁵)/((9x¹²)(8))

 

cancel the 9 in denominator into the 27 in numerator as 3

bring the x¹² in denominator to numerator as x^-12

multiply y¹⁸y⁴⁵ to y⁶³

 

= 3x¹⁸x^-12y⁶³/8

 

= 3x⁶y⁶³/8 = (3/8)x⁶y⁶³