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Select all the expressions that are equivalent to $\frac{8^2}{4^2}$ . $\newline$ Multi-select Choices: $\newline$ (A) $\frac{1}{2^2}$ $\newline$ (B) $2$ $\newline$ (C) $2^2$ $\newline$ (D) $2^0$

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Calculate quartiles and interquartile range

Full solution

Q. Select all the expressions that are equivalent to

\frac{8^2}{4^2}

.

\newline

Multi-select Choices:

\newline

(A)

\frac{1}{2^2}

\newline

(B)

2

\newline

(C)

2^2

\newline

(D)

2^0

Simplify Exponents: Simplify the given expression using the properties of exponents. $\newline$ The expression $\frac{8^2}{4^2}$ can be simplified by recognizing that $8$ is $2^3$ and $4$ is $2^2$ . $\newline$ $\frac{(2^3)^2}{(2^2)^2} = \frac{2^{3*2}}{2^{2*2}} = \frac{2^6}{2^4}$
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ When dividing like bases, subtract the exponents. $\newline$ $2^6 / 2^4 = 2^{(6-4)} = 2^2$
Evaluate Expression: Evaluate the simplified expression. $2^2 = 4$
Compare with Choices: Compare the result with the given choices. $\newline$ The expression $2^2$ is equivalent to $4$ , which matches choice (C) $2^2$ .
Check Other Equivalences: Check the other choices for equivalence. $\newline$ (A) $\frac{1}{2^2} = \frac{1}{4}$ , which is not equal to $4$ . $\newline$ (B) $2$ is not equal to $4$ . $\newline$ (D) $2^0 = 1$ , which is not equal to $4$ .

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