Question

Simplify ((4x)^2 × 2x^3) / x
$\frac{(4x)^{2} \times 2x^{3} }{x}$
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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

Answer:

$32x^4$

Step-by-step explanation:

Given:

$\dfrac{(4x)^2 \times 2x^3}{x}$

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

$\implies \dfrac{4^2x^2 \times 2x^3}{x}$

Simplify 4²:

$\implies \dfrac{16x^2 \times 2x^3}{x}$

Multiply the numbers:

$\implies \dfrac{32x^2x^3}{x}$

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

$\implies \dfrac{32x^{(2+3)}}{x}$

$\implies \dfrac{32x^5}{x}$

$\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies 32x^{(5-1)}$

$\implies 32x^4$