(-2v^7)^3(-4v^2)^4
Simplify.
Can someone help???
^ and then a number is an exponent.
-2^11v^29
Oh oops.. sorry.. wrong answer
CORRECT ANSWER:
-2048v^29
Of course! I'd be happy to help you simplify the expression.
To simplify the expression (-2v^7)^3(-4v^2)^4, we can start by simplifying each base and exponent separately, and then multiply the results. Let's break it down step by step:
First, let's simplify (-2v^7)^3. To raise a negative number or variable to an odd power, we keep the negative sign and raise the absolute value of the base to that power. So, (-2v^7)^3 = (-2)^3 * (v^7)^3.
(-2)^3 is -8, and (v^7)^3 means we raise v^7 to the power of 3, which gives us v^(7*3) = v^21.
Next, let's simplify (-4v^2)^4. To raise a negative number or variable to an even power, the negative sign becomes positive, and we raise the absolute value of the base to that power. So, (-4v^2)^4 = (4^4) * (v^2)^4.
Now, (4^4) means we raise 4 to the power of 4, which gives us 256. And (v^2)^4 means we raise v^2 to the power of 4, which gives us v^(2*4) = v^8.
Finally, we can multiply the simplified bases and exponents: (-2v^7)^3 * (-4v^2)^4 = (-8 * 256) * (v^21 * v^8).
Multiplying the numeric values, we get (-8 * 256) = -2048. And for the variable part, we add the exponents: v^21 * v^8 = v^(21+8) = v^29.
So, the simplified expression is -2048v^29.
I hope this helps! Let me know if you have any other questions.