Question

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

Answer 1

`\\ \rm\Rrightarrow 4^(-2)7^(-2)`

• a^{-n}=1/a^n

`\\ \rm\Rrightarrow (1)/(4^2.7^2)`

• a^n×b^n=(ab)^n

`\\ \rm\Rrightarrow (1)/((4.7)^2)`

`\\ \rm\Rrightarrow (1)/(28^2)`

If we break only 4

`\\ \rm\Rrightarrow (7^(-2))/(4^2)`

Option B and C

Answer 2

`\textsf{B)}\quad (1)/(28^2)`

`\textsf{C)} \quad (7^(-2))/(4^2)`

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)=(1)/(a^n):`

`\implies (1)/(28^2)`

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Also,

`4^(-2) \cdot 7^(-2)`

`\textsf{Apply exponent rule} \quad a^(-n)=(1)/(a^n):`

`\implies (7^(-2))/(4^2)`