Simplify.
(-2b^3 a^2)^5
Write your answer without parentheses
-32b^15 a^10
To simplify (-2b^3 a^2)^5, we can apply the power of a power rule, which states that when you raise a power to another power, you multiply the exponents.
So, (-2b^3 a^2)^5 becomes -2^5 * (b^3)^5 * (a^2)^5.
Simplifying further, we have:
(-2b^3 a^2)^5 = -32 * b^(3*5) * a^(2*5).
This simplifies to:
(-2b^3 a^2)^5 = -32b^15a^10.
Therefore, the simplified expression is -32b^15a^10.
To simplify the given expression, we can apply the power of a power rule. According to this rule, when a base is raised to an exponent and that entire expression is raised to another exponent, the exponents can be multiplied.
In this case, we have (-2b^3 a^2)^5. To simplify, we start by applying the power of a power rule to each term inside the parentheses separately.
First, let's simplify -2^5. When a negative base is raised to an odd power, the result will be negative. So (-2)^5 is equal to -32.
Next, we simplify b^3 raised to the power of 5. When a base with an exponent is raised to another exponent, we multiply the exponents. Therefore, (b^3)^5 is equal to b^(3*5), which is b^15.
Finally, we simplify a^2 raised to the power of 5. Similarly, (a^2)^5 is equal to a^(2*5), which is a^10.
Putting it all together, (-2b^3 a^2)^5 simplifies to -32b^15 a^10.
So, the answer without parentheses is: -32b^15 a^10.