1. simplify the following expression, and rewrite it in an equivalent form with

Question

1. simplify the following expression, and rewrite it in an equivalent form with positive exponents.

10x^2 y^3 / 40x^-3 y^-4

2. Short Answer. Raise the quantity in parentheses to indicate, and simplify the resulting expression. Express answers with positive exponents.

(28xy^3 / 140x^3y^-2)^2

3. Short Answer. Raise the quantity in parentheses to indicate, and simplify the resulting expression. Express answers with positive exponents.

(x^-2y^-1 / 2x^0y^3)^3

4. convert to scientific notation: 0.00694

Explanation / Answer

1. Anything with a negative exponent will turn to a positive exponent if you put it on the bottom if it was on the top, or on the top if it was on the bottom.
EG: 1/(X-1) = x1

Y-4 = 1/Y4

Thus (10(X2)(Y3))/(40(X-3)(Y-4)) = 10(X5)(Y7). <-- Notice that when multiplying the bases with exponents (x and y) You added the exponents. -> (X2)*(X20) = X22

2. For this step, since everything within the parenthesis to be raised to the 2nd power is either multiplication or division, you can carry the 2nd power through each base within.

EG. (10*X*Y)2 = (102)(X2)(Y2)

(10*X5)2 = (102)*(X10)

(X2)3 = X6 <---- note that when raising a number with a power to a power, you multiply the powers.

Use this method, as well as the method from number 1 to solve.

3. Same as 2.

4.

For scientific notation, you simply move the decimal place until you only have one number on the left side of it (1s place) and then multiply it by ten to the power of however many places you moved the decmal, a positive power if you moved the decimal to the left, and a negative power if you moved the decimal to the right.

EG. 123 = 1.23*102

.0062 = 6.2*10-3

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