Question

Jamie evaluated this expression. StartFraction left-bracket (2 cubed) (2) right-bracket Superscript 4 Baseline Over 2 Superscript 10 Baseline Endfraction step 1: StartFraction left-bracket (2 Superscript 4 Baseline) Superscript 4 Baseline Over 2 Superscript 10 EndFraction step 2: StartFraction 2 Superscript 16 Over 2 Superscript 10 EndFraction step 3: 26 step 4: 64 Analyze the steps Jamie applied to evaluate the expression. Which rule of exponents was applied in each step? Step 1: Step 2: Step 3:

Answer 1

(A) PRODUCT OF POWERS

(B) POWER OF A POWER

(C) QUOTIENT OF POWERS

Explanation:

it is correct

Answer 2

1/8

Explanation:

Given the expression

`((2^3)(2)^4)/(2^(10)) \\`

Using the following laws of indices;

`(a^m)/(a^n) = a^(m-n)\\a^m * a^n = a^(m+n)`

The expression becomes;

Step 1: Multiplication rule

`=((2^3)(2)^4)/(2^(10)) \\= (2^(3+4))/(2^(10))\\= (2^7)/(2^(10))`

Using the division rule of exponent (Quotient of powers);

`= (2^7)/(2^(10)) \\= 2^(7-10)\\= 2^(-3)\\also \ a^(-m) = (1)/(a^m)\\ 2^(-3)= (1)/(2^3)\\(1)/(2^3) = (1)/(8)`

Hence the result of the expression is 1/8