Question

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

Answer 1

-112
`c^(14)`

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)`