Question

The expression (-4a^3b)^2the expression -4 to the 3rd power B to the second power is equivalent to ​:______

Answer 1

The expression (-4a^3b)^2 is equivalent to 16a^6b^2, which is found by squaring the coefficient and multiplying the exponents of the variables.

Step-by-step explanation:

The expression (-4a^3b)^2 can be expanded by raising both the coefficient and the variables to the second power. When we raise a number or an expression to a power, it is equivalent to multiplying that number or expression by itself for the number of times indicated by the exponent. In this case, the exponent is 2, which refers to squaring the expression.

To square the expression, we follow the rule that (x^n)^m = x^(n*m), meaning we multiply the exponents. Applying this to our expression, we get:

• Square the coefficient: (-4)^2 = 16
• Square each variable by multiplying the exponents: (a^3)^2 = a^(3*2) = a^6
• Square the last variable: (b)^2 = b^2

Combining the results, we obtain the expanded expression as 16a^6b^2.