Question
The expression for $4^{-3}$ as a power with the base $2$ is $2^6$.
✓
Answer
False.Solution:
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}}$ $\therefore$ $4^{-3}=\frac{1}{4^3}$ $=\frac{1}{(2^2)^3}=\frac{1}{(2)^6}$ $[\because2\times2=4,(\text{a}^\text{m})^\text{n}=(\text{a})^\text{mn}]$
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^\text{m}}$ $\therefore$ $4^{-3}=\frac{1}{4^3}$ $=\frac{1}{(2^2)^3}=\frac{1}{(2)^6}$ $[\because2\times2=4,(\text{a}^\text{m})^\text{n}=(\text{a})^\text{mn}]$
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