Question

Rocky simplified an expression in three steps, as shown below: 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 equals x to the power of 2 times y to the power of negative 4. 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

Answer 1

Step 3 is wrong

Explanation:

Answer 2

The first incorrect step and why include: D. Step 3, the exponents of the same base are added during division.

In Mathematics and Euclidean Geometry, an exponent can be represented or modeled by this mathematical expression;

`b^n`

Where:

• the variables b and n are numbers (numerical values), letters, or an algebraic expression.
• n is known as a superscript or power.

Based on the information provided, we can logically deduce the following expression;

`((x^(-5)y^2)/(yx^3\cdot x^3y^(-5)))^2`

Step 1: First, we would distribute the exponent of 2 as follows;

`((x^(-5)y^2)/(yx^3\cdot x^3y^(-5)))^2\\\\(x^(-5(2))y^(2(2)))/(y^2x^(3(2))\cdot x^(3(2))y^(-5(2)))\\\\(x^(-10)y^(4))/(y^(2)x^(6)\cdot x^(6)y^(-10))`

Step 2: We would combine the exponents in the denominator;

`(x^(-10)y^(4))/(y^(2)x^(6)\cdot x^(6)y^(-10))\\\\(x^(-10)y^(4))/(y^(2-10)x^(6+6))\\\\(x^(-10)y^(4))/(y^(-8)x^(12))`

Step 3: By applying the quotient rule of exponents
`(a^m)/(a^n) =a^(m-n)`, we have;

`(x^(-10)y^(4))/(y^(-8)x^(12))\\\\x^((-10-12))y^((4-(-8)))\\\\x^(-22)y^(12)`

In conclusion, we can logically deduce that the first incorrect step is step 3 because the exponents of the same base were added during division, instead of subtracted.

Complete Question;

Rocky simplified an expression in three steps, as shown:

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