Question

If x>0, what is the product of 7 square root of 5x³?

Answer 1

For a positive value of x, the product of 7 square root of 5x³ is 7x¹±²(5¹±²), which simplifies to the expression involving the multiplication of 7, x, and 5 raised to various powers.

Step-by-step explanation:

If x>0, the product of 7 square root of 5x³ would be calculated by first looking at the properties of exponents and roots. According to the rules for handling exponents:

• We interpret the square root of 5x³ as 5x³ raised to the 1/2 power, because multiplying the square root of a number by itself yields the original number, just like x² = √x.

• When multiplying powers with the same base, we simply add the exponents, so for instance, x¹x¹ = x±±.

Applying this knowledge to our problem:

(7)(√5x³) = 7(5x³)¹² = 7x³²¹/² = 7x¹¹²(5¹±²)

Assuming x is a positive real number, this is the simplified expression for the product.