To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so subtract the coefficients and retain the base and exponent:

-1x⁴ - 7x⁴
(-1 - 7)x⁴
-8x⁴

The yearly interest charged on this loan is the annual interest rate multiplied by the amount borrowed:

interest = annual interest rate x loan amount

i = (\( \frac{6}{100} \)) x $1,400
i = 0.06 x $1,400

No payments were made so the total amount due is the original amount + the accumulated interest:

The least common multiple (LCM) is the smallest positive integer that is a multiple of two or more integers.

First, solve for \( \left|x - 9\right| \):

\( \left|x - 9\right| \) + 7 = -7
\( \left|x - 9\right| \) = -7 - 7
\( \left|x - 9\right| \) = -14

The value inside the absolute value brackets can be either positive or negative so (x - 9) must equal - 14 or --14 for \( \left|x - 9\right| \) to equal -14:

So, x = 23 or x = -5.

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 72 are [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]. They share 4 factors [1, 2, 4, 8] making 8 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{72} \) = \( \frac{\frac{16}{8}}{\frac{72}{8}} \) = \( \frac{2}{9} \)