Question

Simplify the Expression (4x³)² using the properties of integer exponents
8x⁶
4x⁶
16x⁵
16x⁶

Answer 1

Using the property of integer exponents, when raising a power to a power, you multiply the exponents.

In this case, you have (4x³)², which means you are raising 4x³ to the power of 2.

Therefore, you get (4x³)² = 4² * (x³)² = 16 * x⁶.

So the simplified expression is 16x⁶.

Answer 2

Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x⁴y-⁴)³/(x⁷y³)²
64/x²⁰
X²y¹⁸/64
64/x²y¹⁸
4/x²y¹⁸

Answer 3

To generate an equivalent expression using the properties of integer exponents, we can simplify each part and apply the rules of exponents.

First, let's simplify (4x⁴y⁻⁴)³:
(4x⁴y⁻⁴)³ = 4³ * (x⁴)³ * (y⁻⁴)³ = 64x¹² * y⁻¹²

Next, let's simplify (x⁷y³)²:
(x⁷y³)² = (x⁷)² * (y³)² = x¹⁴ * y⁶

Now, we can divide (4x⁴y⁻⁴)³ by (x⁷y³)²:
(4x⁴y⁻⁴)³ / (x⁷y³)² = (64x¹² * y⁻¹²) / (x¹⁴ * y⁶)

Applying the quotient rule of exponents, we subtract the exponents when dividing:
= 64x¹²⁻¹⁴ * y⁻¹²⁻⁶ = 64x⁻²² * y⁻¹⁸

Hence, the equivalent algebraic expression is 64/x²²y¹⁸, which can also be rewritten as 64/x²y¹⁸.