Simplify: (5d3)(-2d2)

Sergeant Math 8 Multiplying Monomials

1) Simplify: (m⁴)²

To simplify (m^4)^2, we need to apply the exponent rule which states that when raising a power to a power, we multiply the exponents. In this case, we have m^4 raised to the power of 2. Multiplying the exponents 4 and 2 gives us m^8. Therefore, the simplified form of (m^4)^2 is m^8.

Explanation

To simplify (m^4)^2, we need to apply the exponent rule which states that when raising a power to a power, we multiply the exponents. In this case, we have m^4 raised to the power of 2. Multiplying the exponents 4 and 2 gives us m^8. Therefore, the simplified form of (m^4)^2 is m^8.

2) Simplify: (n⁵)(n²)(m³)(m⁴)

The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables with the same base. In this case, the expression can be simplified to n^7 * m^7, where n has an exponent of 7 and m has an exponent of 7.

Explanation

The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables with the same base. In this case, the expression can be simplified to n^7 * m^7, where n has an exponent of 7 and m has an exponent of 7.

3) Simplify: (5d³)(-2d²)

10

-10

10

-10

The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables. In this case, (5d3)(-2d2) simplifies to -10d^5, where the coefficient is -10 and the exponent of the variable d is 5. Therefore, the answer is -10.

Explanation

The given expression can be simplified by multiplying the coefficients and adding the exponents of the variables. In this case, (5d3)(-2d2) simplifies to -10d^5, where the coefficient is -10 and the exponent of the variable d is 5. Therefore, the answer is -10.

4) Simplify: (

1 fourth

c d cubed

right parenthesis squared

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Explanation

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5) Simplify: 5x²(5²x³)

The expression can be simplified using the order of operations, which states that multiplication should be done before addition or subtraction. First, we solve the multiplication within the parentheses: 52x3 = 156. Then, we multiply this result by 5x2 = 10. Therefore, the simplified expression is 10(156) = 1560.

Explanation

The expression can be simplified using the order of operations, which states that multiplication should be done before addition or subtraction. First, we solve the multiplication within the parentheses: 52x3 = 156. Then, we multiply this result by 5x2 = 10. Therefore, the simplified expression is 10(156) = 1560.