Simplify each expression. Write answers using positive exponents.
a. (7x^2y^3)(-2xy)
b. (a^2b^3)^-1(a^2b^3)
c.(-4m^3)^2
To simplify each expression, we can apply the rules of exponents. Here's how you can solve each problem:
a. (7x^2y^3)(-2xy)
To simplify this expression, you need to multiply the coefficients and combine the variables with the same base raised to different exponents.
So, you can calculate the coefficient as (-2)*(7) = -14.
Then, since both variables have the base x, you can combine them by adding their exponents: x^2 * x^1 = x^(2+1) = x^3.
Similarly, you can combine the variables with the base y: y^3 * y^1 = y^(3+1) = y^4.
Therefore, the simplified expression is -14x^3y^4.
b. (a^2b^3)^-1(a^2b^3)
To simplify this expression, you need to apply the rule of negative exponents and raise a number to the power of -1, which is equivalent to finding its reciprocal.
The expression (a^2b^3)^-1 is equivalent to 1 / (a^2b^3).
Now you can multiply this expression by (a^2b^3) to get (1 / (a^2b^3)) * (a^2b^3).
When you multiply these two terms, you will see that (a^2b^3) cancels out with (a^2b^3), and you are left with 1, because any number divided by itself is 1.
Therefore, the simplified expression is 1.
c. (-4m^3)^2
To simplify this expression, you need to apply the power of a power rule. In this case, you raise the base of -4m^3 to the power of 2, which means you multiply the exponents.
So, you square the -4 and square the m^3, which results in 16m^6.
Therefore, the simplified expression is 16m^6.