Question

Harold starts to simplify the expression below, as shown, but his work is not correct. –x(6x⁵)2(–2y⁶)(y) (–6x⁶)2(–2y⁶)(y) What should Harold have done instead?

a. Combined like terms

b. Squared 6x⁵

c. Used the foil method

d. Squared 6x⁶

Answer 1

Harold should have applied the exponent to each base and its associated power in the expression, adhering to the rules of exponents for squaring and multiplying exponential terms.

Step-by-step explanation:

Harold is tasked with simplifying the mathematical expression –x(6x⁵)2(–2y⁶)(y) (–6x⁶)2(–2y⁶)(y). The expression involves exponents and multiplication, therefore the correct approach would be to square 6x⁵ and square 6x⁶, as he needs to apply the exponent to the base and its associated power. Additionally, when dealing with powers of products, the rule is to raise each factor to the power. For instance, (a*b)^n equals a^n*b^n. Furthermore, when multiplying exponential terms with the base, we add the exponents. Therefore, Harold should have used these rules to simplify the expression rather than combining like terms or using the FOIL method.