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

Answer:

1/8

Step-by-step explanation:

Given the expression

$\frac{(2^3)(2)^4}{2^{10}}$

Using the following laws of indices;

$\frac{a^m}{a^n} = a^{m-n}\\a^m \times a^n = a^{m+n}$

The expression becomes;

Step 1: Multiplication rule

$=\frac{(2^3)(2)^4}{2^{10}} \\= \frac{2^{3+4}}{2^{10}}\\= \frac{2^7}{2^{10}}$

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

$= \frac{2^7}{2^{10}} \\= 2^{7-10}\\= 2^{-3}\\also \ a^{-m} = \frac{1}{a^m}\\ 2^{-3}= \frac{1}{2^3}\\\frac{1}{2^3} = \frac{1}{8}$

Hence the result of the expression is 1/8

Answer 2

Answer:

(A) PRODUCT OF POWERS

(B) POWER OF A POWER

(C) QUOTIENT OF POWERS

Step-by-step explanation:

it is correct