Simplify each expression. ( − 2 x 4 y 5 ) 4 (-2x^4y^5)^4

Here, we're going to simplify the expression negative two times x to the fourth power times y to the fifth power all raised to the fourth power. And we're going to do this using our power of a product rule by distributing in our outside exponent of four into each of the factors in this product. And here we actually have four factors. We have negative one, two, x to the fourth power, and y to the fifth power. So distributing that in, we'll have negative one to the fourth power times two to the fourth power times x to the fourth to the fourth power, times y to the fifth, also to the fourth power. Next, let's evaluate our constants. Negative one to the fourth power will become a positive one since our exponent is even. So we'll have just one multiplied by two to the fourth power evaluates to 16. X to the fourth to the fourth power, we can use our power rule and multiply our exponents. So we'll get x to the sixteenth power. And using the same rule for our last term, y to the fifth to the fourth power, we'll multiply our exponents and get y to the twentieth power. Now, anything multiplied by one is just one, so we'll rewrite our final answer as 16 x to the sixteenth times y to the twentieth. And that's our expression in its simplest form.

Simplify each expression. ( − 2 x 4 y 5 ) 4 (-2x^4y^5)^4

− 16 x 16 y 20 -16x^{16}y^{20}

6. Exponents, Polynomials, and Polynomial Functions

Intro to the Power Rules

Intermediate Algebra

6. Exponents, Polynomials, and Polynomial Functions

Intro to the Power Rules

Struggling with Intermediate Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Simplify each expression.
$(- 2 x^{4} y^{5})^{4}$

$- 16 x^{16} y^{20}$

$2 x^{16} y^{20}$

$16 x^{16} y^{20}$

$8x^8y^9$

Verified step by step guidance

Identify the expression to simplify: $(-2x^{4}y^{5})^{4}$. This means the entire quantity inside the parentheses is raised to the 4th power.

Apply the power of a product rule: When a product inside parentheses is raised to a power, raise each factor to that power separately. So rewrite as $(-2)^{4} \cdot (x^{4})^{4} \cdot (y^{5})^{4}$.

Use the power of a power rule for the variables: $(x^{4})^{4} = x^{4 \times 4} = x^{16}$ and $(y^{5})^{4} = y^{5 \times 4} = y^{20}$.

Calculate the coefficient raised to the power: $(-2)^{4}$. Remember that an even power of a negative number results in a positive number.

Combine all parts to write the simplified expression as the product of the coefficient and the variables with their new exponents: \$16x^{16}y^{20}$.

3:08m

Watch next

Master The Power Rule for Exponents with a bite sized video explanation from Patrick Ford

Start learning

Struggling with Intermediate Algebra?

Simplify each expression.(−2x4y5)4(-2x^4y^5)^4

Watch next

Simplify each expression.
$(- 2 x^{4} y^{5})^{4}$