Question

Simplify the expression. can anyone explain to me how to do this? please

Answer 1

Answer:

last option 32x⁷y¹⁵ is the correct answer.

Step-by-step explanation:

Identities

1). (xᵃ)ᵇ = xᵃᵇ

2). xᵃxᵇ = x⁽ᵃ⁺ ᵇ)

To find the value of expression

The given expression is,

(x²)(2xy³)⁵

Using the above identities we can evaluate the value of expression

⇒ (x²)*(2)⁵ *(x)⁵ * (y³)⁵

⇒ (2)⁵ * (x²) *(x)⁵ *(y³)⁵

⇒  32* (x²⁺⁵) *(y³ˣ⁵)

⇒  32 * x⁷ *y¹⁵

⇒  32x⁷y¹⁵

Therefore last option 32x⁷y¹⁵ is the correct answer.

Answer 2

Answer:

The answer is the last one (32x^7y^15)

You can bring x to the second power (x^2) because (x) is basically x^1. This is a basic exponent rule. (x^m)^n = x^m times n.

Then you can apply this rule to (2xy^3)^5. First you bring two to the fifth power and get 32. Then you bring x^5 according to the rule. Then you bring y^15, also because of the rule.

Now you have:

x^2 times 32x^5y^15

Now you just multiply the like terms together (x^2 and x^5)

When you multiply two exponents with the same base, you add the exponents together: a^n times a^m = a^n+m.

So you end up with 32x^7y^15