Solutions to Test#1

The solutions for the test problems are not numbered because of the three different forms.

This problem requires the property of adding exponents for the same bases when the bases are multiplied.

The property for dividing like bases and subtracting exponents is used here.

The property of raising an exponent to an exponent by distributing the exponent (-2) across all bases including the coefficient is applied along with knowing to move a variable to either the denominator or numerator (based on its location) to make it positive.

The airplane-airport distance is an application of the Pythagorean Theorem.

becomes or So, b = 13709.5 ft or 100 ft.

Order of operations follow the pneumonic: Please Excuse My Dear Aunt Sally (moving left to right).

Subtraction changes all signs.

Squaring a binomial

Use the Distributive Property of Multiplication and add like terms.

Factor by grouping and the sum of a perfect cube

or 3(4x+3)(4x+3) Remove the common factor to find a perfect square trinomial where you take the square root of the first and last terms and keep the sign of the middle term. This can be checked using FOIL.

This problem divides two rational expressions, which means that multiplying by the reciprocal of the divisor gives the result we want. So, factor the difference of squares and divide out the common factors before simplifying.

To add rational expressions we must have a common denominator and that requires us to multiply the second fraction by 1 in the form of before adding and simplifying.

To simplify a complex fraction, multiply both the numerator and denominator by the reciprocal of the denominator in the original complex expression and simplify.

Taking the square root of an expression involves two things: the coefficient where we remove the largest perfect square number as a factor and bring it outside the radical. The variable exponents are then multiplied by ½.

To rationalize the numerator/denominator with a radical addition or subtraction, multiply both the numerator and denominator by the conjugate and simplify.

This product is of the same base, p, so we add the two fractional powers by getting a common denominator. 2x2 is not affected by this exponent because it is on the base p only. The radical form is as shown because the denominator is the index of the radical and the numerator is the power on p in the radical.