Question

What makes this statement true? 7^-2

Answer 1

For this case we have:

By definition, one of the properties of the power, known as negative integer power, states that:

$a ^{-b}$can be written as$\frac{1}{a ^ b}$

Thus,  $7 ^{-2}$ can be written as $\frac{1}{7 ^ 2}$ . So:

$\frac{1}{7 ^ 2}= \frac{1}{(7 * 7)}=\frac{1}{49}$

Answer:

Power of negative integer exponent:

$7^{-2} =\frac{1}{7 ^ 2}= \frac{1}{(7 * 7)}=\frac{1}{49}$

Answer 2

The negative power means 1/the number to the given power

This means that 7^-2 can be rewritten as 1/(7^2)
7^2 = 7*7
Therefore:
1/(7^2) = 1/(7*7)
7*7 = 49
Therefore:
1/(7*7) = 1/49

Based on the above calculations:
7^-2 is equal to 1/49