Simplify the Expression (4x³)² using the properties of integer exponents
8x⁶
4x⁶
16x⁵
16x⁶
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.
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
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.
To simplify the expression (4x³)² using the properties of integer exponents, you would multiply the exponents inside the parentheses by the exponent outside the parentheses.
In this case, the exponent outside the parentheses is 2, so you would multiply 3 (the exponent of x) by 2.
3 * 2 = 6.
Therefore, the simplified expression is 16x⁶.
To simplify the expression (4x³)² using the properties of integer exponents, we can apply the power of a power rule.
The power of a power rule states that when you raise a power to another power, you multiply the exponents. In this case, we need to multiply the exponent inside the parentheses (3) with the exponent outside the parentheses (2).
So, we have:
(4x³)² = 4² * (x³)²
Taking the power of 4 yields:
4² = 16
For the variable x, we multiply the exponents:
(x³)² = x^(3*2)
Simplifying the exponent inside the parentheses:
(x³)² = x⁶
Hence, the simplified expression is:
(4x³)² = 16x⁶
Therefore, the correct answer is 16x⁶.