Question

Write as a monomial in standard form (−4x^2ya^3)^2

Answer 1

Answer:

16x⁴y²a⁶

Step-by-step explanation:

(−4x²ya³)^2

(-4)² × (x²)² + (y)² × (a³)²

16 × x⁴ × y² × a⁶

16x⁴y²a⁶

Answer 2

The given monomial in standard form is $16a^6x^4y^2$

Solution:

A Monomial in standard form is the product of one or more factors: a constant coefficient and one factor for each variable in the expression.

Given monomial is:

$(-4x^2ya^3)^2$

We use the following law of exponents to solve the above monomial:

$(ab)^n = a^nb^n\\\\(a^n)^m = a^{mn}$

Using these in given monomial, we get

$(-4x^2ya^3)^2 = (-4)^2(x^2)^2(y)^2(a^3)^2$

Now applying the law of exponent $(a^n)^m = a^{mn}$ we get,

$(-4)^2(x^2)^2(y)^2(a^3)^2 = 16x^{2 \times 2}y^2a^{3 \times 2} = 16x^4y^2a^6$

A monomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc

Writing in standard form we get,

$\rightarrow 16a^6x^4y^2$

Thus the given monomial is written in standard form