Rocky simplified an expression in three steps, as shown:

x to the power of negative 5 multiplied by y to the power of 2, over y multiplied by x to the power of 3 multiplied by x to the power of 3 multiplied by y to the power of negative 5, the whole to the power of 2 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of 2 multiplied by x to the power of 6 multiplied by x to the power of 6 multiplied by y to the power of negative 10 equals x to the power of negative 10 multiplied by y to the power of 4, over y to the power of negative 8 multiplied by x to the power of 12.

Which is the first incorrect step and why?

Step 1, all the exponents are increased by 2
Step 1, all the exponents are multiplied by 2
Step 2, the exponents in the denominator are added during multiplication
Step 3, the exponents of the same base are added during division

Step three is wrong because when you divide use the quotient rule which is in division the exponents are subtracted and in this problem the exponents are added

Answer Link

erinna erinna · Answer 2 · 2019-10-11T13:41:54+02:00

Answer:

Step 3.

Step-by-step explanation:

The given expression is

[tex](\frac{x^{-5}y^2}{yx^3\cdot x^3y^{-5}})^2[/tex]

Step 1: Using distributive property of exponent we get

[tex]\frac{(x^{-5})^2(y^2)^2}{(y)^2(x^3)^2\cdot (x^3y^{-5})^2}[/tex] [tex][\because (ab)^x=a^xb^x][/tex]

[tex]\frac{x^{-10}y^4}{y^2x^6\cdot x^6y^{-10}}[/tex]

Ste 2: Using product property of exponent, we get

[tex]\frac{x^{-10}y^4}{y^{2-10}x^{6+6}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]

[tex]\frac{x^{-10}y^4}{y^{-8}x^{12}}[/tex]

Step 3: Using quotient property of exponent, we get

[tex]x^{(-10-12)}y^{4-(-8)}[/tex] [tex][\because \frac{a^m}{a^n}=a^{m-n}][/tex]

[tex]x^{(-22)}y^{12}[/tex]

Therefore, the first incorrect step is 3.