Question

i.14 identify equivalent expressions involving exponents msn
select all the expressions that are equivalent to $2^2 \cdot 6^2$.
$\frac{1}{12^2}$ $12^2$ $\frac{1}{12^{-2}}$ $12^4$
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not feeling ready yet? these can help:
negative exponents (100) multiplication with exponents - variable bases (100)
division with exponents - variable bases (100) power rule - variable bases (100)

Explanation:

Step1: Recall exponent rule \(a^m \cdot b^m=(ab)^m\)

For \(2^2 \cdot 6^2\), apply the rule: \((2\times6)^2 = 12^2\).

Step2: Recall negative exponent rule \(a^{-n}=\frac{1}{a^n}\)

\(12^2\) can be written as \(\frac{1}{12^{-2}}\) (since \(12^2=\frac{1}{12^{-2}}\) by \(a^n=\frac{1}{a^{-n}}\)).

Step3: Analyze incorrect options

• \(12^4\) is not equivalent as \(2^2\cdot6^2 = 12^2

eq12^4\).

• \(\frac{1}{12^2}\) is \(12^{-2}\), not equivalent to \(12^2\).

Answer:

The equivalent expressions are \(12^2\) and \(\frac{1}{12^{-2}}\) (i.e., the options with \(12^2\) and \(\frac{1}{12^{-2}}\) should be selected, and the others are incorrect. So the correct selections are the second (\(12^2\)) and third (\(\frac{1}{12^{-2}}\)) options).