Exponents with Variables Worksheets

Are you a middle school or high school student struggling with exponents and variables in math? If so, you're in the right place! In this blog post, we will explore the benefits of using worksheets to practice and improve your skills in solving equations involving exponents and variables. Whether you're looking to strengthen your knowledge or prepare for an upcoming test, these worksheets will provide you with ample practice and reinforcement.

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  Fraction Decimal Word Problems 6th Grade

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  Fraction Decimal Word Problems 6th Grade

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  Fraction Decimal Word Problems 6th Grade

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  Fraction Decimal Word Problems 6th Grade

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  Fraction Decimal Word Problems 6th Grade

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What is the exponent of a variable in the expression 5x^3?

The exponent of the variable in the expression 5x^3 is 3.

Simplify the expression 4x^2 y^3 / x^3 y^2.

To simplify the expression 4x^2 y^3 / x^3 y^2, we can cancel out common factors in the numerator and the denominator. Since x^2/x^3 = 1/x and y^3/y^2 = y, the simplified form is 4y/x.

Expand the expression (2a^2 b^3)^4.

The expression (2a^2 b^3)^4 expands to 16a^8 b^12.

Evaluate the expression 3x^2 + 2x - 5 for x = 4.

Substitute x = 4 into the expression 3x^2 + 2x - 5 to evaluate it. We get 3(4)^2 + 2(4) - 5 = 3(16) + 8 - 5 = 48 + 8 - 5 = 51. Therefore, the value of 3x^2 + 2x - 5 for x = 4 is 51.

Solve the equation 2x^3 = 16.

To solve the equation 2x^3 = 16, you first need to isolate x by dividing both sides by 2 to get x^3 = 8. Then, taking the cube root of both sides gives you x = 2. Therefore, the solution to the equation is x = 2.

Simplify the expression (3ab^2)^2 (2a^2 b)^3.

The simplified expression is 108a^7 b^8.

Simplify the expression (3x^2 y^3)^4 / (9x^4 y^2).

First, expand the expression (3x^2 y^3)^4 to get 81x^8 y^12. Now, divide 81x^8 y^12 by 9x^4 y^2 to get 9x^(8-4) y^(12-2) = 9x^4 y^10. Therefore, the simplified expression is 9x^4 y^10.

In the expression 7xy^3 / (2x^2 y), what is the quotient?

The quotient of 7xy^3 divided by 2x^2 y is 3.5y^2 / x.

Solve the equation (4a^2 b^3)^2 = 64.

To solve the equation (4a^2 b^3)^2 = 64, we need to first expand the expression inside the parentheses, which gives us 16a^4 b^6. Then, we have (16a^4 b^6)^2 = 64. Simplifying further, we get 256a^8 b^12 = 64. Dividing by 64 on both sides gives us a^8 b^12 = 1/4. Therefore, the solution to the equation is a^8 b^12 = 1/4.

Simplify the expression (x^2 + 2xy + y^2)(x - y)^2.

The simplified expression is x^5 - 3x^4y + 3x^3y^2 - 3x^2y^3 + y^4.