Answer:
[tex]\frac{1}{7^7}[/tex] ≈ [tex]1.21*10^{-6}[/tex]
Step-by-step explanation:
Our equation is [tex]\frac{7^{-6}}{7}[/tex] . 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:
[tex]\frac{7^{-6}}{7}=\frac{1}{7^6*7}[/tex]
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:
[tex]\frac{1}{7^6*7}=\frac{1}{7^{6+1}} =\frac{1}{7^7}[/tex]
If we want to find the decimal expansion of this, it is around: [tex]1.21*10^{-6}[/tex] (in scientific notation).
Hope this helps!
