Question

simplify each expression by multiplying monomials: -7c^8 * (-4c^3)^2

Answer 1

Answer:

-112$c^{14}$

Step-by-step explanation:

-7$c^{8}$ $(-4c^{3}) ^{2}$ in expanded form this would be

-7cccccccc-4ccc-4ccc rearranged with like factors together

-7-4-4cccccccccccccc

For the numbers, count the negative signs.  It the sum is an even number than the product is positive.  If the sum is a negative number, then the product is negative.  There are a total of 3 negative signs.  This is a odd number so the product is negative

-112$c^{14}$   There are a total of 14 c's

Or

You could use the power rules.

When a power is raised to a power.  The exponent goes to every factor in the parentheses.

$(-4)^{2}$ $(c^{3}) ^{2}$  -4 times -4 is 16 The power of power property tells us that when a power is raised to a power we multiply the exponents so we now have

16$c^{6}$  When we multiple this by -7$c^{8}$  We multiply 16 x -7 which is -112.  The product of powers principle tells us that when we multiply powers with the same bases, we add the exponents.

-112$c^{14}$