Question

Simplify ((4x)^2 × 2x^3) / x

`((4x)^(2) * 2x^(3) )/(x)`
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Answer 1

(4x)^2 • 2x^3/ x

Cancel the common factor of x^3 and x

x (( 4x )^2 • ( 2x )^2 ) / x
Cancel the common factor

( 4x )^2 • ( 2x )^2

Rewrite using the commutative property of multiplication.

2 ( 4x )^2•x^2

Apply the product rule to 4x

2 ( 4^2 • x^2 ) x^2

Multiply x^2 by x^2 adding exponents

2 ( 4^2 x^4 )

Raise 4 to power of 2

2 ( 16x^4 )

Multiply 16 by 2

32x^4

Answer 2

`32x^4`

Explanation:

Given:

`((4x)^2 * 2x^3)/(x)`

`\textsf{Apply exponent rule} \quad (ab)^c=a^cb^c:`

`\implies (4^2x^2 * 2x^3)/(x)`

Simplify 4²:

`\implies (16x^2 * 2x^3)/(x)`

Multiply the numbers:

`\implies (32x^2x^3)/(x)`

`\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^(b+c):`

`\implies (32x^((2+3)))/(x)`

`\implies (32x^5)/(x)`

`\textsf{Apply exponent rule} \quad (a^b)/(a^c)=a^(b-c):`

`\implies 32x^((5-1))`

`\implies 32x^4`