Question

Simplify the quantity negative 7 times a to the 3rd power times b to the negative 3 power end quantity divided by the quantity 21 times a times b end quantity. −3a2b4 negative one times the quantity 3 times a squared end quantity divided by b to the fourth power negative one times a squared divided by the quantity 3 times b to the fourth power end quantity negative one times a squared divided by the quantity 3 times b to the second power

Answer 1

To simplify expressions with exponents, apply the power of a quotient and negative exponent rules. Rewrite negative exponents as positive exponents in the denominator and subtract exponents when dividing like bases.

Step-by-step explanation:

When simplifying algebraic expressions with exponents, it is important to understand the rules of exponents such as the power of a quotient rule and the negative exponent rule. These rules are essential for manipulating expressions effectively. The power of a quotient rule indicates that when you have a power applied to a quotient, you apply the power to both the numerator and the denominator:
(x/y)a = xa/ya.

The negative exponent rule states that a negative exponent indicates that the base should be taken as 1 divided by that base raised to the positive form of the exponent: x-a = 1/xa. Using these rules, we can simplify given algebraic expressions by applying the correct operations step by step.