Question

What is the quotient ? StartFraction 7 Superscript negative 6 Over 7 squared EndFraction

Answer 1

Answer:

7^(-8) or 1/7⁸

Step-by-step explanation:

(7^-6)/7²

7^(-6-2)

7^(-8) or

1/7⁸

Answer 2

Answer:

$\frac{1}{7^7}$ ≈ $1.21*10^{-6}$

Step-by-step explanation:

Our equation is $\frac{7^{-6}}{7}$ . Whenever we have a negative exponent, we can turn it positive by moving it from the numerator to the denominator or vice versa (depending on where it's located). Here, 7^(-6) is in the numerator so we can then move it to the denominator and make it positive:

$\frac{7^{-6}}{7}=\frac{1}{7^6*7}$

Remember that when multiplying powers with the same base (in this case, that shared base is 7), we can combine them into one by adding the exponents. Here, we have 7^6 (exponent is 6) and 7 (exponent is 1). So:

$\frac{1}{7^6*7}=\frac{1}{7^{6+1}} =\frac{1}{7^7}$

If we want to find the decimal expansion of this, it is around: $1.21*10^{-6}$ (in scientific notation).

Hope this helps!