Question

Simplify, assuming that no denominator is equal to zero: (a⁵b³)(a³b⁵)

a) a⁸b⁸
b) a¹5b¹5
c) a⁸b¹5
d) a¹5b⁸

Answer 1

When simplifying (a⁵b³)(a³b⁵), the exponents for each base are added together, resulting in a⁸b⁸. The correct answer is a) a⁸b⁸.

Step-by-step explanation:

The question involves simplifying an expression with exponents by multiplying two exponential terms together. To simplify (a⁵b³)(a³b⁵), we use the rule of multiplying exponents, which states that we add exponents when multiplying like bases. Therefore, the simplified form would be a⁵+³b³+⁵, which is a⁸b⁸. The correct answer is option a) a⁸b⁸.

Using the given examples, we can see that when multiplying exponential terms like (5³)⁴ or (7⁴)³, we simply multiply the exponents together. In the current problem, since the bases a and b are the same in both terms, all we need to do is add the exponents for each base.

Answer 2

To simplify (a⁵b³)(a³b⁵), you add the exponents of like bases: a⁵ * a³ = a⁸ and b³ * b⁵ = b⁸, resulting in a⁸b⁸.The correct option is A.

Step-by-step explanation:

To simplify the expression (a⁵b³)(a³b⁵), you need to apply the rule for multiplying powers with the same base. According to the rules of exponents, when you multiply two terms with the same base, you add their exponents. So for the bases a and b, the exponents will be added separately.

For the base a:

• a⁵ * a³ = a^(5+3) = a⁸

For the base b:

• b³ * b⁵ = b^(3+5) = b⁸

Therefore, the simplified form of (a⁵b³)(a³b⁵) is a⁸b⁸, which corresponds to option a) a⁸b⁸.