Question

which expressions are equivalent to 4^-2*7^-2

Answer 1

Answer:

$\textsf{B)}\quad \dfrac{1}{28^2}$

$\textsf{C)} \quad \dfrac{7^{-2}}{4^2}$

Step-by-step explanation:

$4^{-2} \cdot 7^{-2}$

$\textsf{Apply exponent rule} \quad (a^b \cdot c^b)=(ac)^b:$

$\implies (4 \cdot 7)^{-2}$

$\implies (28)^{-2}$

$\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:$

$\implies \dfrac{1}{28^2}$

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Also,

$4^{-2} \cdot 7^{-2}$

$\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:$

$\implies \dfrac{7^{-2}}{4^2}$

Answer 2

$\\ \rm\Rrightarrow 4^{-2}7^{-2}$

• a^{-n}=1/a^n

$\\ \rm\Rrightarrow \dfrac{1}{4^2.7^2}$

• a^n×b^n=(ab)^n

$\\ \rm\Rrightarrow \dfrac{1}{(4.7)^2}$

$\\ \rm\Rrightarrow \dfrac{1}{28^2}$

If we break only 4

$\\ \rm\Rrightarrow \dfrac{7^{-2}}{4^2}$

Option B and C